scholarly journals Prime, weakly prime and almost prime elements in multiplication lattice modules

2016 ◽  
Vol 14 (1) ◽  
pp. 673-680
Author(s):  
Emel Aslankarayigit Ugurlu ◽  
Fethi Callialp ◽  
Unsal Tekir
Keyword(s):  
Prime Element ◽  
Idempotent Element ◽  
Prime Elements ◽  
Almost Prime

AbstractIn this paper, we study multiplication lattice modules. We establish a new multiplication over elements of a multiplication lattice module.With this multiplication, we characterize idempotent element, prime element, weakly prime element and almost prime element in multiplication lattice modules.

scholarly journals ϕ-Prime and ϕ-Primary Elements in Multiplicative Lattices

Algebra ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
C. S. Manjarekar ◽  
A. V. Bingi
Keyword(s):  
Multiplicative Lattice ◽  
Primary Element ◽  
Prime Elements ◽  
Compactly Generated ◽  
Almost Prime ◽  
Multiplicative Lattices

We investigate ϕ-prime and ϕ-primary elements in a compactly generated multiplicative lattice L. By a counterexample, it is shown that a ϕ-primary element in L need not be primary. Some characterizations of ϕ-primary and ϕ-prime elements in L are obtained. Finally, some results for almost prime and almost primary elements in L with characterizations are obtained.

scholarly journals Weakly unique factorization modules

2010 ◽  
Vol 41 (3) ◽  
pp. 245-252
Author(s):  
Kursat Hakan Oral ◽  
Unsal Tekir ◽  
Ahmet Goksel Agargun
Keyword(s):  
Prime Element ◽  
Unique Factorization ◽  
Prime Submodules ◽  
Definition Of ◽  
Prime Elements

In this work we give the definition of weakly prime element of a module. Therefore we give a new definition of factorization in a module, which is called weakly factorization. So we call a module weakly unique factorization module if all elements have a weakly factorization which is unique. We give the relation between weakly prime elements and weakly prime submodules. Then we characterize such weakly unique factorization modules.

scholarly journals φ-Prime and φ-Primary Elements in Lattice Modules

2021 ◽  
Vol 14 (2) ◽  
pp. 551-577
Author(s):  
Ashok V. Bingi ◽  
C. S. Manjarekar
Keyword(s):  
Prime Element ◽  
Primary Element ◽  
Almost Prime

In this paper, we introduce φ-prime and φ-primary  elements in an L-module M. Many of its characterizations and properties are obtained. By counter examples, it is shown that a φ-prime element of M need not be prime, a φ-primary element of M need not be φ-prime, a φ-primary element of M need not be prime and a φ-primary element of M need not be primary. Finally, some results for almost prime and almost primary elements of an L-module M with their characterizations are obtained. Also, we introduce the notions of n-potent prime (respectively n-potent primary) elements in L and M to obtain interrelations among them where n≥2. 

Materialism and Legal Historiography, from Bachelard to Benjamin

2019 ◽  
pp. 1-19
Author(s):  
Christopher Tomlins
Keyword(s):  
Walter Benjamin ◽  
Historical Materialism ◽  
First Century ◽  
Gaston Bachelard ◽  
Spatial Justice ◽  
Legal Studies ◽  
New Materialisms ◽  
The World ◽  
Prime Elements ◽  
Cultural Turn

As the linguistic/cultural turn of the last fifty years has begun to ebb, sociolegal and legal-humanist scholarship has seen an accelerating return to materiality. This chapter asks what relationship may be forthcoming between the “new materialisms” and “vibrant matter” of recent years, and the older materialisms—both historical and literary, both Marxist and non-Marxist—that held sway prior to post-structuralism. What impact might such a relationship have on the forms, notably “spatial justice,” that materiality is assuming in contemporary legal studies? To attempt answers, the chapter turns to two figures from more than half a century ago: Gaston Bachelard—once famous, now mostly forgotten; and Walter Benjamin—once largely forgotten, now famous. A prolific and much-admired writer between 1930 and 1960, Bachelard pursued two trajectories of inquiry: a dialectical and materialist and historical (but non-Marxist) philosophy of science; and a poetics of the material imagination based on inquiry into the literary reception and representation of the prime elements—earth, water, fire, and air. Between the late 1920s and 1940, meanwhile, Benjamin developed an idiosyncratic but potent form of historical materialism dedicated to “arousing [the world] from its dream of itself.” The chapter argues that by mobilizing Bachelard and Benjamin for scholarship at the intersection of law and the humanities, old and new materialisms can be brought into a satisfying conjunction that simultaneously offers a poetics for spatial justice and lays a foundation for a materialist legal historiography for the twenty-first century.

scholarly journals A note on Noetherian orders in Artinian rings

1979 ◽  
Vol 20 (2) ◽  
pp. 125-128 ◽  
Author(s):  
A. W. Chatters
Keyword(s):  
Noetherian Ring ◽  
Quotient Ring ◽  
Triangular Matrix ◽  
Idempotent Element ◽  
Noetherian Rings ◽  
Central Idempotent ◽  
Matrix Rings ◽  
Regular Elements ◽  
Zero Divisors ◽  
Left And Right

Throughout this note, rings are associative with identity element but are not necessarily commutative. Let R be a left and right Noetherian ring which has an Artinian (classical) quotient ring. It was shown by S. M. Ginn and P. B. Moss [2, Theorem 10] that there is a central idempotent element e of R such that eR is the largest Artinian ideal of R. We shall extend this result, using a different method of proof, to show that the idempotent e is also related to the socle of R/N (where N, throughout, denotes the largest nilpotent ideal of R) and to the intersection of all the principal right (or left) ideals of R generated by regular elements (i.e. by elements which are not zero-divisors). There are many examples of left and right Noetherian rings with Artinian quotient rings, e.g. commutative Noetherian rings in which all the associated primes of zero are minimal together with full or triangular matrix rings over such rings. It was shown by L. W. Small that if R is any left and right Noetherian ring then R has an Artinian quotient ring if and only if the regular elements of R are precisely the elements c of R such that c + N is a regular element of R/N (for further details and examples see [5] and [6]). By the largest Artinian ideal of R we mean the sum of all the Artinian right ideals of R, and it was shown by T. H. Lenagan in [3] that this coincides in any left and right Noetherian ring R with the sum of all the Artinian left ideals of R.

scholarly journals ON NEAR-RING IDEMPOTENTS AND POLYNOMIALS ON DIRECT PRODUCTS OF Ω-GROUPS

2001 ◽  
Vol 44 (2) ◽  
pp. 379-388 ◽  
Author(s):  
Erhard Aichinger
Keyword(s):  
Direct Product ◽  
Subject Classification ◽  
Idempotent Element ◽  
Direct Products ◽  
Primary 16Y30 ◽  
Secondary 08A40

AbstractLet $N$ be a zero-symmetric near-ring with identity, and let $\sGa$ be a faithful tame $N$-group. We characterize those ideals of $\sGa$ that are the range of some idempotent element of $N$. Using these idempotents, we show that the polynomials on the direct product of the finite $\sOm$-groups $V_1,V_2,\dots,V_n$ can be studied componentwise if and only if $\prod_{i=1}^nV_i$ has no skew congruences.AMS 2000 Mathematics subject classification: Primary 16Y30. Secondary 08A40

scholarly journals Reductions of an elliptic curve with almost prime orders

2005 ◽  
Vol 119 (3) ◽  
pp. 265-289 ◽  
Author(s):  
Alina Carmen Cojocaru
Keyword(s):  
Elliptic Curve ◽  
Almost Prime
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