A Characterization of *-Congruences on a Regular *-Semigroup

1998 ◽  
Vol 56 (3) ◽  
pp. 442-445 ◽  
Author(s):  
Younki Chae ◽  
Sang Youl Lee ◽  
Chan-Young Park
Keyword(s):  
Regular Semigroup

scholarly journals Ideal Theory in Semigroups Based on Intersectional Soft Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Seok Zun Song ◽  
Hee Sik Kim ◽  
Young Bae Jun
Keyword(s):  
Regular Semigroup ◽  
Ideal Theory ◽  
Soft Sets

The notions of int-soft semigroups and int-soft left (resp., right) ideals are introduced, and several properties are investigated. Using these notions and the notion of inclusive set, characterizations of subsemigroups and left (resp., right) ideals are considered. Using the notion of int-soft products, characterizations of int-soft semigroups and int-soft left (resp., right) ideals are discussed. We prove that the soft intersection of int-soft left (resp., right) ideals (resp., int-soft semigroups) is also int-soft left (resp., right) ideals (resp., int-soft semigroups). The concept of int-soft quasi-ideals is also introduced, and characterization of a regular semigroup is discussed.

scholarly journals A characterization of Commutative Semigroups

2021 ◽  
Vol 12 (3) ◽  
pp. 5150-5155
Author(s):  
Dr. D. Mrudula Devi Et. al.
Keyword(s):  
Inverse Semigroup ◽  
Regular Semigroup ◽  
Commutative Semigroup ◽  
Zero Semigroup ◽  
Completely Regular Semigroup ◽  
Semi Group ◽  
Commutative Semigroups ◽  
Completely Regular ◽  
Left Regular

This paper deals with some results on commutative semigroups. We consider (s,.) is externally commutative right zero semigroup is regular if it is intra regular and (s,.) is externally commutative semigroup then every inverse semigroup  is u – inverse semigroup. We will also prove that if (S,.) is a H -  semigroup then weakly cancellative laws hold in H - semigroup. In one case we will take (S,.) is commutative left regular semi group and we will prove that (S,.) is ∏ - inverse semigroup. We will also consider (S,.) is commutative weakly balanced semigroup  and then prove every left (right) regular semigroup is weakly separate, quasi separate and separate. Additionally, if (S,.) is completely regular semigroup we will prove that (S,.) is permutable and weakly separtive. One a conclusing note we will show and prove some theorems related to permutable semigroups and GC commutative Semigroups.

scholarly journals Group congruences on eventually regular semigroups

1988 ◽  
Vol 45 (3) ◽  
pp. 320-325 ◽  
Author(s):  
S. Hanumantha Rao ◽  
P. Lakshmi
Keyword(s):  
Regular Semigroup ◽  
Group Congruence ◽  
Regular Semigroups ◽  
Eventually Regular Semigroup ◽  
Lattice Of Congruences

AbstractA characterization of group congruences on an eventually regular semigroup S is provided. It is shown that a group congruence is dually right modular in the lattice of congruences on S. Also for any group congruence ℸ and any congruence p on S, ℸ Vp and kernel ℸ Vp are described.

scholarly journals Unit regular inverse monoids and Cliford monoids

2018 ◽  
Vol 7 (2.13) ◽  
pp. 306
Author(s):  
Sreeja V K
Keyword(s):  
Inverse Semigroup ◽  
Regular Semigroup ◽  
Group Element ◽  
Inverse Monoid ◽  
Completely Regular Semigroup ◽  
Clifford Semigroup ◽  
Inverse Monoids ◽  
Completely Regular ◽  
Group Of Units

Let S be a unit regular semigroup with group of units G = G(S) and semilattice of idempotents E = E(S). Then for every there is a such that Then both xu and ux are idempotents and we can write or .Thus every element of a unit regular inverse monoid is a product of a group element and an idempotent. It is evident that every L-class and every R-class contains exactly one idempotent where L and R are two of Greens relations. Since inverse monoids are R unipotent, every element of a unit regular inverse monoid can be written as s = eu where the idempotent part e is unique and u is a unit. A completely regular semigroup is a semigroup in which every element is in some subgroup of the semigroup. A Clifford semigroup is a completely regular inverse semigroup. Characterization of unit regular inverse monoids in terms of the group of units and the semilattice of idempotents is a problem often attempted and in this direction we have studied the structure of unit regular inverse monoids and Clifford monoids. 

scholarly journals Free completely regular semigroups

1984 ◽  
Vol 25 (2) ◽  
pp. 241-254 ◽  
Author(s):  
P. G. Trotter
Keyword(s):  
Regular Semigroup ◽  
Structure Theory ◽  
Completely Regular Semigroup ◽  
Regular Semigroups ◽  
Completely Regular ◽  
Additional Operation ◽  
Alternative Characterization ◽  
Completely Regular Semigroups

A completely regular semigroup is a semigroup that is a union of groups. The aim here is to provide an alternative characterization of the free completely regular semigroup Fcrx on a set X to that given by J. A. Gerhard in [3, 4].Although the structure theory for completely regular semigroups was initiated in 1941 [1] by A. H. Clifford it was not until 1968 that it was shown by D. B. McAlister [5] that Fcrx exists. More recently, in [7], M. Petrich demonstrated the existence of Fcrx by showing that completely regular semigroups form a variety of unary semigroups (that is, semigroups with the additional operation of inversion).

scholarly journals Characterization of regular semigroup by (∈, ∈∨(k*, q_k))-fuzzy ideals

2017 ◽  
Vol 13 (3) ◽  
pp. 403-419 ◽  
Author(s):  
Muhammad Sajjad Ali Khan ◽  
Khaista Rahman ◽  
Syed Zaheer Abbas ◽  
Saleem Abdullah
Keyword(s):  
Regular Semigroup

scholarly journals Normal partitions of idempotents of regular semigroups

1978 ◽  
Vol 26 (1) ◽  
pp. 110-114 ◽  
Author(s):  
P. G. Trotter
Keyword(s):  
Regular Semigroup ◽  
Subject Classification ◽  
Regular Semigroups ◽  
M 10 ◽  
20 M 10

AbstractA characterization is provided here for any normal partition of the set of idempotents of a regular semigroup S. As a by-product of the method used, a new characterization of the greatest congruence on S corresponding to a given normal partition of its idempotents is obtained.Subject classification (Amer. Math. Soc. (MOS) 1970): 20 M 10.

scholarly journals Skew Pairs of Idempotents in Partial Transformation Semigroups

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 2
Author(s):  
Panuwat Luangchaisri ◽  
Thawhat Changphas
Keyword(s):  
Regular Semigroup ◽  
Transformation Semigroup ◽  
Acta Math ◽  
Partial Transformation ◽  
Transformation Semigroups ◽  
Full Transformation ◽  
Full Transformation Semigroup ◽  
Left Regular

Let S be a regular semigroup. A pair (e,f) of idempotents of S is said to be a skew pair of idempotents if fe is idempotent, but ef is not. T. S. Blyth and M. H. Almeida (T. S. Blyth and M. H. Almeida, skew pair of idempotents in transformation semigroups, Acta Math. Sin. (English Series), 22 (2006), 1705–1714) gave a characterization of four types of skew pairs—those that are strong, left regular, right regular, and discrete—existing in a full transformation semigroup T(X). In this paper, we do in this line for partial transformation semigroups.

V-regular semigroups

1981 ◽  
Vol 88 (3-4) ◽  
pp. 275-291 ◽  
Author(s):  
K. S. S. Nambooripad ◽  
F. Pastijn
Keyword(s):  
Regular Semigroup ◽  
Transformation Semigroup ◽  
Inverse Semigroups ◽  
Full Transformation ◽  
Regular Semigroups ◽  
Von Neumann ◽  
Biordered Set ◽  
Von Neumann Regular ◽  
Strongly Regular

SynopsisA regular semigroup S is called V-regular if for any elements a, b ∈ S and any inverse (ab)′ of ab, there exists an inverse a′ of a and an inverse b′ of b such that (ab)′ = b′a′. A characterization of a V-regular semigroup is given in terms of its partial band of idempotents. The strongly V-regular semigroups form a subclass of the class of V-regular semigroups which may be characterized in terms of their biordered set of idempotents. It is shown that the class of strongly V-regular semigroups comprises the elementary rectangular bands of inverse semigroups (including the completely simple semigroups), a special class of orthodox semigroups (including the inverse semigroups), the strongly regular Baer semigroups (including the semigroups that are the multiplicative semigroup of a von Neumann regular ring), the full transformation semigroup on a set, and the semigroup of all partial transformations on a set.

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

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