scholarly journals On the union of graded prime ideals

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 114-118 ◽  
Author(s):  
Rabia Nagehan Uregen ◽  
Unsal Tekir ◽  
Kursat Hakan Oral
Keyword(s):  
Integral Domain ◽  
Prime Ideals ◽  
The Family ◽  
Graded Integral Domain ◽  
As If

AbstractIn this paper we investigate graded compactly packed rings, which is defined as; if any graded ideal I of R is contained in the union of a family of graded prime ideals of R, then I is actually contained in one of the graded prime ideals of the family. We give some characterizations of graded compactly packed rings. Further, we examine this property on h – Spec(R). We also define a generalization of graded compactly packed rings, the graded coprimely packed rings. We show that R is a graded compactly packed ring if and only if R is a graded coprimely packed ring whenever R be a graded integral domain and h – dim R = 1.

Graded integral domains in which each nonzero homogeneous t-ideal is divisorial

2019 ◽  
Vol 18 (01) ◽  
pp. 1950018 ◽  
Author(s):  
Gyu Whan Chang ◽  
Haleh Hamdi ◽  
Parviz Sahandi
Keyword(s):  
Integral Domain ◽  
Nonzero Ideal ◽  
Integral Domains ◽  
Cancellative Monoid ◽  
Integrally Closed ◽  
Graded Integral Domain

Let [Formula: see text] be a nonzero commutative cancellative monoid (written additively), [Formula: see text] be a [Formula: see text]-graded integral domain with [Formula: see text] for all [Formula: see text], and [Formula: see text]. In this paper, we study graded integral domains in which each nonzero homogeneous [Formula: see text]-ideal (respectively, homogeneous [Formula: see text]-ideal) is divisorial. Among other things, we show that if [Formula: see text] is integrally closed, then [Formula: see text] is a P[Formula: see text]MD in which each nonzero homogeneous [Formula: see text]-ideal is divisorial if and only if each nonzero ideal of [Formula: see text] is divisorial, if and only if each nonzero homogeneous [Formula: see text]-ideal of [Formula: see text] is divisorial.

scholarly journals PREWEDDING PHOTO PROCESSION AND THE ROLE OF THE FAMILY IN THEM

2020 ◽  
Vol 10 (2) ◽  
pp. 246
Author(s):  
Aulil Amri
Keyword(s):  
Islamic Law ◽  
Religious Values ◽  
Religious Knowledge ◽  
The Family ◽  
Marriage Contract ◽  
The Law ◽  
Husband And Wife ◽  
As If

In Islamic law, pre-wedding photos have not been regulated in detail. However, pre-wedding photo activities have become commonplace by the community. It becomes a problem when pre-wedding is currently done with an intimate scene, usually the prospective bride uses sexy clothes and is also not accompanied by her mahram when doing pre-wedding photos. Even though there have been many fatwas and studies on the limits of permissibility and prohibition in the pre-wedding procession.The results show that the pre-wedding procession that is carried out by the community in terms of poses, clothes, and also assistance in accordance with Islamic law, the law is permissible. However, it often happens in the community to take photos before the marriage contract with scenes as if they are legally husband and wife and the bride's family knows without prohibiting, directing, and guiding them according to Islamic teachings. In this case the role of the family is very important, we as parents must understand the basis of religious knowledge and how to instill religious values in our children since childhood is the key to this problem dilemma.

scholarly journals A PRESENÇA DE ESCRAVOS EM ALGUNS CONTOS DE MACHADO DE ASSIS

2018 ◽  
Vol 2 ◽  
pp. 160
Author(s):  
Antonio Marcos Sanseverino
Keyword(s):  
Nineteenth Century ◽  
Rio De Janeiro ◽  
Daily Life ◽  
Personal History ◽  
Machado De Assis ◽  
Brazilian Literature ◽  
The Family ◽  
As If

A escravidão é o nexo fundamental para pensar a literatura brasileira do século XIX. Na prosa machadiana, esse nexo histórico foi evidenciado por diferentes críticos (CHALHOUB, 2003, 2012; GLEDSON, 2006; SCHWARZ, 2000). Na leitura dos jornais, desde os anos de 1870, através da leitura de anúncios, vemos o quanto a presença do escravo doméstico era fato naturalizado no cotidiano do Rio de Janeiro (FREYRE, 2012; SCHWARCZ, 1987). Amas, copeiros, cozinheiros, moleques eram anunciados como objeto de venda ou de aluguel. Não apenas o trabalho era vendido ou alugado, mas o próprio trabalhar-escravo. Essa presença cotidiana de escravos é necessária (ou não) para a compreensão dos enredos? Alguns contos machadianos que trazem à primeiro plano do conflito a presença da escravidão: “Mariana” (1871), “O caso da vara” (1899) e “Pai contra mãe” (1906). Entretanto, há um apagamento da história pessoal do escravo enquanto personagem. A expressão “cria da casa” usada para caracterizar Mariana, uma mulata que vive como fosse da família, mostra o quanto a genealogia da personagem se apaga, diluída no pertencimento à casa do dono. Palavras-chave: Machado de Assis. Escravidão. Conto. Cria da casa.ABSTRACTSlavery is the fundamental link to think of nineteenth-century Brazilian literature. In Machado’s prose, this historical nexus was evidenced by different critics (CHALHOUB, 2003, 2012, GLEDSON, 2006, SCHWARZ, 2000). In the reading of the newspapers, from the 1870s, through the reading of advertisements, we see how the presence of the domestic slave was a naturalized fact in the daily life of Rio de Janeiro (FREYRE, 2012; SCHWARCZ, 1987). Mothers, cupbearers, cooks, brats were advertised as objects for sale or rent. Not only was work sold or rented, but the work-slave itself. Is this daily presence of slaves necessary (or not) for the understanding of entanglements? Some Machado tales that bring to the forefront of the conflict the presence of slavery: “Mariana” (1871), “The case of the stick” (1899) and “Father against mother” (1906). However, there is an erasure of the slave’s personal history as a character. The expression “housekeeper” used to characterize Mariana, a mulatta who lives as if she were one of the family, shows how much the character’s genealogy is extinguished, diluted in belonging to the owner’s house.Keywords: Machado de Assis. Slavery. Tale. Of the house.

scholarly journals A Translation into English of Khalil I. Al-Fuzai’s1“In the Café”2

2018 ◽  
Vol 6 (6) ◽  
Author(s):  
Gassim H. Dohal
Keyword(s):  
Good Life ◽  
Saudi Arabian ◽  
Human Being ◽  
The Family ◽  
State Of Mind ◽  
Pain And Suffering ◽  
Islamic Faith ◽  
The Village ◽  
As If ◽  
At Home

One of the principles of the Islamic faith is belief in destiny; “that Allah has power over all things and that Allah surrounds all things in (His) knowledge” (Al-Hilali 768). A human being does not have knowledge of his/her predestination, and thus acts in accordance with a choice and/or a desire from within him. Yet some people in the Saudi Arabian society blame destiny for their idleness as if fate were their problem. They should not attribute their laziness to destiny because Islam requires people to work, and their fate is unknown to them before it takes place. This story portrays how luck or fate can play an important role in the life of some people. The protagonist goes to the café to spend time and drink some coffee. There he gets acquainted with his rich uncle, who had left the village. While introducing the story setting, the author uses such words as “routine,” “mechanical,” “dull,” “gloom,” “boring,” etc.— words that reflect the protagonist’s state of mind, and how he envisions his life; it is a difficult and miserable life. Though he apparently goes to the café for a change of pace from the dull atmosphere at home, boredom follows him everywhere. Yousef is “alone to face the hardships of life....”; even in the café, he is alienated. So he wishes to marry, because a wife, as a partner, would support him, at least emotionally; but he questions “how can *I+ afford marriage expenses?” in a society where marriage requires wealth. He is no different from other main characters in this collection who are struggling to earn a living. Like Hassan, the protagonist of “Before the Station,” Yousef in this story assumes his late father’s responsibilities; he should “make a living for his mother and his two littlem brothers....3 ” The Saudi Arabian society expects the elder son to take care of the family if something bad happens to the father and, at the same time; it rarely provides any support for such families. Hence, Yousef should “become a sailor” who will face the “tyrannical cruelty” of the sea that delivered the deathblow to his father. He has no idea that his life will end up with such a struggle. It is Um-Kalthoom, a famous Arabian singer, whose songs give him momentum to struggle for survival. To him, she creates “an immortal melody” about pain and suffering—“a pleasant song chanted by sad people” like him. And as long as she manages to mold pain into “a pleasant song” between her lips, he has a chance to create a good life for his family out of the hardships he is facing through his daily struggle. Indeed, “a new dawn in *Yousef’s+ life” emerges after a lengthy night, and his fall changes into spring. While he is sitting in the café, a coincidence takes place: an old, rich man appears, looking for his nephew who, in the end, turns out to be Yousef himself. As is the case in “A Point of Change,” the author depicts in this story difficulties of living, and how chance or fate, as people there call it, may change one’s life.

ROLE OF THE COURTS

PEDIATRICS ◽  
1973 ◽  
Vol 51 (4) ◽  
pp. 796-798
Author(s):  
Florence M. Kelley
Keyword(s):  
Social Work ◽  
Juvenile Court ◽  
Family Court ◽  
Court System ◽  
The Family ◽  
Long Time ◽  
Neglected Children ◽  
Abused And Neglected Children ◽  
As If

It is important to know what the courts can do and cannot do in the area of abused and neglected children. Often the Family Court is listed as an agency. It is not an agency. It is part of the court system. Its operation is circumscribed by the concept of being a real court. For a long time there was a theory that the Family Court or Juvenile Court could be a kind of social work oriented operation, not quite a real court, not truly a social work agency. This concept has been abandoned. The Family Court is a court of record and is in all aspects a court. It is dependent in the action it takes on evidence which must conform to strict rules that are laid down. It is an adversary proceeding. It is not enough to produce a child that looks as if it has been beaten. A judge in the Family Court also has before him the person who may be charged with having beaten the child. That person, be it a parent or guardian, is entitled to counsel, to help in his defense. The adversary process then takes place. Persons bring forth evidence to show that the parent did abuse the child. The parent is enabled under the court system to bring forth before the judge evidence that he or she did not do it. It is then up to the judge to give this evidence due weight and make a decision as to whether or not the allegations have been proven.

Factoring Ideals into Semiprime Ideals

1978 ◽  
Vol 30 (6) ◽  
pp. 1313-1318 ◽  
Author(s):  
N. H. Vaughan ◽  
R. W. Yeagy
Keyword(s):  
Integral Domain ◽  
Dedekind Domain ◽  
Prime Ideals ◽  
Semiprime Ideal ◽  
Dedekind Domains

Let D be an integral domain with 1 ≠ 0 . We consider “property SP” in D, which is that every ideal is a product of semiprime ideals. (A semiprime ideal is equal to its radical.) It is natural to consider property SP after studying Dedekind domains, which involve factoring ideals into prime ideals. We prove that a domain D with property SP is almost Dedekind, and we give an example of a nonnoetherian almost Dedekind domain with property SP.

Adoption in Ethiopia Ten Years after the Civil Code

1972 ◽  
Vol 16 (2) ◽  
pp. 145-168 ◽  
Author(s):  
John H. Beckstrom
Keyword(s):  
Civil Code ◽  
Family Unit ◽  
The Family ◽  
Mutual Interest ◽  
Close Friendship ◽  
As If

Forms by which children born outside a family unit are taken into the family have existed since time immemorial in Ethiopia. These forms have varied depending upon the ethnic, religious and regional groupings involved. The relationships created range from rather loose affirmations of close friendship and mutual interest to complete assimilation of the outsider as if he had been born within the family. This article will be concerned only with the later type of customary assimilation, which we will term “adoption”.

Some Properties of Noetherian Domains of Dimension One

1961 ◽  
Vol 13 ◽  
pp. 569-586 ◽  
Author(s):  
Eben Matlis
Keyword(s):  
Vector Space ◽  
Integral Domain ◽  
Chain Condition ◽  
Prime Ideals ◽  
Quotient Field ◽  
Rank One ◽  
Descending Chain Condition ◽  
A Chain ◽  
Dimension One ◽  
Torsion Free

Throughout this discussion R will be an integral domain with quotient field Q and K = Q/R ≠ 0. If A is an R-module, then A is said to be torsion-free (resp. divisible), if for every r ≠ 0 ∈ R the endomorphism of A defined by x → rx, x ∈ A, is a monomorphism (resp. epimorphism). If A is torsion-free, the rank of A is defined to be the dimension over Q of the vector space A ⊗R Q; (we note that a torsion-free R-module of rank one is the same thing as a non-zero R-submodule of Q). A will be said to be indecomposable, if A has no proper, non-zero, direct summands. We shall say that A has D.C.C., if A satisfies the descending chain condition for submodules. By dim R we shall mean the maximal length of a chain of prime ideals in R.

scholarly journals On 2-absorbing ideals of commutative rings

2007 ◽  
Vol 75 (3) ◽  
pp. 417-429 ◽  
Author(s):  
Ayman Badawi
Keyword(s):  
Prime Ideal ◽  
Maximal Ideal ◽  
Integral Domain ◽  
Commutative Rings ◽  
Dedekind Domain ◽  
Proper Ideal ◽  
Prime Ideals ◽  
Maximal Ideals ◽  
Noetherian Domain ◽  
Valuation Domains

Suppose that R is a commutative ring with 1 ≠ 0. In this paper, we introduce the concept of 2-absorbing ideal which is a generalisation of prime ideal. A nonzero proper ideal I of R is called a 2-absorbing ideal of R if whenever a, b, c ∈ R and abc ∈ I, then ab ∈ I or ac ∈ I or bc ∈ I. It is shown that a nonzero proper ideal I of R is a 2-absorbing ideal if and only if whenever I1I2I3 ⊆ I for some ideals I1,I2,I3 of R, then I1I2 ⊆ I or I2I3 ⊆ I or I1I3 ⊆ I. It is shown that if I is a 2-absorbing ideal of R, then either Rad(I) is a prime ideal of R or Rad(I) = P1 ⋂ P2 where P1,P2 are the only distinct prime ideals of R that are minimal over I. Rings with the property that every nonzero proper ideal is a 2-absorbing ideal are characterised. All 2-absorbing ideals of valuation domains and Prüfer domains are completely described. It is shown that a Noetherian domain R is a Dedekind domain if and only if a 2-absorbing ideal of R is either a maximal ideal of R or M2 for some maximal ideal M of R or M1M2 where M1,M2 are some maximal ideals of R. If RM is Noetherian for each maximal ideal M of R, then it is shown that an integral domain R is an almost Dedekind domain if and only if a 2-absorbing ideal of R is either a maximal ideal of R or M2 for some maximal ideal M of R or M1M2 where M1,M2 are some maximal ideals of R.

scholarly journals The distribution of prime ideals of a Dedekind domain

1974 ◽  
Vol 11 (3) ◽  
pp. 429-441 ◽  
Author(s):  
Anne P. Grams
Keyword(s):  
Class Group ◽  
Sufficient Conditions ◽  
Torsion Group ◽  
Dedekind Domain ◽  
Necessary And Sufficient Conditions ◽  
Prime Ideals ◽  
Class Groups ◽  
Maximal Ideals ◽  
The Family ◽  
Necessary And Sufficient

Let G be an abelian group, and let S be a subset of G. Necessary and sufficient conditions on G and S are given in order that there should exist a Dedekind domain D with class group G with the property that S is the set of classes that contain maximal ideals of D. If G is a torsion group, then S is the set of classes containing the maximal ideals of D if and only if S generates G. These results are used to determine necessary and sufficient conditions on a family {Hλ} of subgroups of G in order that there should exist a Dedekind domain D with class group G such that {G/Hλ} is the family of class groups of the set of overrings of D. Several applications are given.

Sign in / Sign up

Export Citation Format

Share Document