scholarly journals Endomorphisms of Clifford semigroups with injective structure homomorphisms

2020 ◽  
Vol 30 (2) ◽  
pp. 290-304
Author(s):  
S. Worawiset ◽  
◽  
J. Koppitz ◽  
Keyword(s):  
Proper Subgroup ◽  
Endomorphism Monoid ◽  
Clifford Semigroup ◽  
Completely Regular ◽  
Clifford Semigroups

In the present paper, we study semigroups of endomorphisms on Clifford semigroups with injective structure homomorphisms, where the semilattice has a least element. We describe such Clifford semigroups having a regular endomorphism monoid. If the endomorphism monoid on the Clifford semigroup is completely regular then the corresponding semilattice has at most two elements. We characterize all Clifford semigroups Gα∪Gβ (α>β) with an injective structure homomorphism, where Gα has no proper subgroup, such that the endomorphism monoid is completely regular. In particular, we consider the case that the structure homomorphism is bijective.

scholarly journals Generalized Neutrosophic Extended Triplet Group

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 327 ◽  
Author(s):  
Yingcang Ma ◽  
Xiaohong Zhang ◽  
Xiaofei Yang ◽  
Xin Zhou
Keyword(s):  
Regular Semigroup ◽  
Algebraic System ◽  
Classical Group ◽  
Algebra Structure ◽  
Completely Regular Semigroup ◽  
Single Factor ◽  
Clifford Semigroup ◽  
Completely Regular ◽  
Group 4

Neutrosophic extended triplet group is a new algebra structure and is different from the classical group. In this paper, the notion of generalized neutrosophic extended triplet group is proposed and some properties are discussed. In particular, the following conclusions are strictly proved: (1) an algebraic system is a generalized neutrosophic extended triplet group if and only if it is a quasi-completely regular semigroup; (2) an algebraic system is a weak commutative generalized neutrosophic extended triplet group if and only if it is a quasi-Clifford semigroup; (3) for each n ∈ Z + , n ≥ 2 , ( Z n , ⊗ ) is a commutative generalized neutrosophic extended triplet group; (4) for each n ∈ Z + , n ≥ 2 , ( Z n , ⊗ ) is a commutative neutrosophic extended triplet group if and only if n = p 1 p 2 ⋯ p m , i.e., the factorization of n has only single factor.

C*-algebras of Clifford semigroups

1989 ◽  
Vol 111 (1-2) ◽  
pp. 129-145 ◽  
Author(s):  
John Duncan ◽  
A.L.T. Paterson
Keyword(s):  
Representation Theory ◽  
Clifford Semigroup ◽  
Sheaf Theory ◽  
C Algebras ◽  
Clifford Semigroups

SynopsisWe investigate algebras associated with a (discrete) Clifford semigroup S =∪ {Ge: e ∈ E{. We show that the representation theory for S is determined by an enveloping Clifford semigroup UC(S) =∪ {Gx: x ∈ X} where X is the filter completion of the semilattice E. We describe the representation theory in terms of both disintegration theory and sheaf theory.

scholarly journals On continuity of homomorphisms between topological Clifford semigroups

2014 ◽  
Vol 6 (1) ◽  
pp. 123-129
Author(s):  
I. Pastukhova
Keyword(s):  
Clifford Semigroup ◽  
Clifford Semigroups ◽  
Topological Clifford Semigroup

Generalizing an old result of Bowman we prove that a homomorphism $f:X\to Y$ between topological Clifford semigroups is continuous if the idempotent band $E_X=\{x\in X:xx=x\}$ of $X$ is a $V$-semilattice;the topological Clifford semigroup $Y$ is ditopological;the restriction $f|E_X$ is continuous;for each subgroup $H\subset X$ the restriction $f|H$ is continuous.

Boolean Congruence Lattices of Orthodox Semigroups

1991 ◽  
Vol 43 (2) ◽  
pp. 225-241 ◽  
Author(s):  
Karl Auinger
Keyword(s):  
Inverse Semigroups ◽  
Regular Semigroups ◽  
Commutative Semigroups ◽  
Completely Regular ◽  
Clifford Semigroups ◽  
Congruence Lattices ◽  
Completely Regular Semigroups ◽  
Orthodox Semigroups

The problem of characterizing the semigroups with Boolean congruence lattices has been solved for several classes of semigroups. Hamilton [9] and the author of this paper [1] studied the question for semilattices. Hamilton and Nordahl [10] considered commutative semigroups, Fountain and Lockley [7,8] solved the problem for Clifford semigroups and idempotent semigroups, in [1] the author generalized their results to completely regular semigroups. Finally, Zhitomirskiy [19] studied the question for inverse semigroups.

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 End-Completely-Regular and End-Inverse Lexicographic Products of Graphs

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Hailong Hou ◽  
Rui Gu
Keyword(s):  
Bipartite Graphs ◽  
Endomorphism Monoid ◽  
Regular Graphs ◽  
Completely Regular

A graphXis said to be End-completely-regular (resp., End-inverse) if its endomorphism monoid End(X) is completely regular (resp., inverse). In this paper, we will show that ifX[Y] is End-completely-regular (resp., End-inverse), then bothXandYare End-completely-regular (resp., End-inverse). We give several approaches to construct new End-completely-regular graphs by means of the lexicographic products of two graphs with certain conditions. In particular, we determine the End-completely-regular and End-inverse lexicographic products of bipartite graphs.

GLOBAL DETERMINISM OF CLIFFORD SEMIGROUPS

2014 ◽  
Vol 97 (1) ◽  
pp. 63-77 ◽  
Author(s):  
AIPING GAN ◽  
XIANZHONG ZHAO
Keyword(s):  
Semigroup Forum ◽  
Clifford Semigroup ◽  
Clifford Semigroups ◽  
Global Determinism

AbstractIn this paper we shall give characterizations of the closed subsemigroups of a Clifford semigroup. Also, we shall show that the class of all Clifford semigroups satisfies the strong isomorphism property and so is globally determined. Thus the results obtained by Kobayashi [‘Semilattices are globally determined’, Semigroup Forum29 (1984), 217–222] and by Gould and Iskra [‘Globally determined classes of semigroups’ Semigroup Forum28 (1984), 1–11] are generalized.

Weak containment and Clifford semigroups

1978 ◽  
Vol 81 (1-2) ◽  
pp. 23-30 ◽  
Author(s):  
Alan L. T. Paterson
Keyword(s):  
Regular Representation ◽  
Positive Definite ◽  
Positive Definite Functions ◽  
Clifford Semigroup ◽  
Clifford Semigroups ◽  
Weak Containment ◽  
Left Regular Representation ◽  
Left Regular

SynopsisLet S be a Clifford semigroup with identity. The weak containment question is posed for S, and answered affirmatively when each of the maximal groups Se in S is amenable. The amenability of S itself is characterised in terms of PL(S), the set of normalised positive definite functions on S arising from the left regular representation of S. A type of mean associated with PL(S) and satisfying a condition weaker than left invariance is introduced.

scholarly journals On the lattice of varieties of completely regular semigroups

1983 ◽  
Vol 35 (2) ◽  
pp. 227-235 ◽  
Author(s):  
P. R. Jones
Keyword(s):  
Lattice Of Varieties ◽  
Regular Semigroups ◽  
Completely Regular ◽  
Variety Of Groups ◽  
Completely Regular Semigroups ◽  
Subdirect Products

AbstractSeveral morphisms of this lattice V(CR) are found, leading to decompostions of it, and various sublattices, into subdirect products of interval sublattices. For example the map V → V ∪ G (where G is the variety of groups) is shown to be a retraction of V(CR); from modularity of the lattice V(BG) of varieties of bands of groups it follows that the map V → (V ∪ V V G) is an isomorphism of V(BG).

scholarly journals Complete regularity of Ellis semigroups of -actions

2020 ◽  
pp. 1-17
Author(s):  
MARCY BARGE ◽  
JOHANNES KELLENDONK
Keyword(s):  
Complete Regularity ◽  
Completely Regular ◽  
Ellis Semigroup ◽  
Totally Disconnected

Abstract It is shown that the Ellis semigroup of a $\mathbb Z$ -action on a compact totally disconnected space is completely regular if and only if forward proximality coincides with forward asymptoticity and backward proximality coincides with backward asymptoticity. Furthermore, the Ellis semigroup of a $\mathbb Z$ - or $\mathbb R$ -action for which forward proximality and backward proximality are transitive relations is shown to have at most two left minimal ideals. Finally, the notion of near simplicity of the Ellis semigroup is introduced and related to the above.

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