On the maximal semilattice decomposition of the power semigroup of a semigroup

1977 ◽  
Vol 15 (1) ◽  
pp. 263-267 ◽  
Author(s):  
Mohan S. Putcha
Keyword(s):  
Power Semigroup ◽  
Semilattice Decomposition

Semilattice decomposition ofn (2)-permutable semigroups

1993 ◽  
Vol 46 (1) ◽  
pp. 16-20 ◽  
Author(s):  
Attila Nagy
Keyword(s):  
Semilattice Decomposition

scholarly journals The maximal semilattice decomposition of a semigroup

1963 ◽  
Vol 69 (3) ◽  
pp. 342-345 ◽  
Author(s):  
Mario Petrich
Keyword(s):  
Semilattice Decomposition

scholarly journals The maximal semilattice decomposition of a semigroup

1964 ◽  
Vol 85 (1) ◽  
pp. 68-82 ◽  
Author(s):  
Mario Petrich
Keyword(s):  
Semilattice Decomposition

scholarly journals A semilattice decomposition into semigroups having at most one idempotent

1971 ◽  
Vol 39 (1) ◽  
pp. 225-228 ◽  
Author(s):  
Mohan Putcha ◽  
Julian Weissglass
Keyword(s):  
Semilattice Decomposition

A note on the power semigroup of a completely simple semigroup

2008 ◽  
Vol 76 (3) ◽  
pp. 584-586 ◽  
Author(s):  
Benjamin Steinberg
Keyword(s):  
Simple Semigroup ◽  
Completely Simple Semigroup ◽  
Power Semigroup ◽  
Completely Simple

scholarly journals On the greatest semilattice decomposition of a semigroup

1955 ◽  
Vol 7 (2) ◽  
pp. 59-62 ◽  
Author(s):  
Miyuki Yamada
Keyword(s):  
Semilattice Decomposition

On Semilattices of R-Ample Semigroups with Left Central Idempotents

2014 ◽  
Vol 530-531 ◽  
pp. 617-620
Author(s):  
Yan Sun
Keyword(s):  
Structure Theorem ◽  
Characterization Theorem ◽  
Ample Semigroup ◽  
Clifford Semigroups ◽  
Semilattice Decomposition ◽  
Strong Semilattice

In this article, the semilattice decomposition of r-ample semigroups with left central idempotents is given. By using this decomposition, we show that a semigroup is a r-ample semigroup with left central idempotents if and only if it is a strong semilattice of , where is a monoid and is a right zero band. As a corollary, the characterization theorem of Clifford semigroups is also extended from a strong semilattice of groups to a strong semilattice of right groups. These theories are the basis that the structure theorem of r-ample semigroups with left central idempotents can be established.

Semilattice Decomposition of Locally Associative AG**-groupoids

2009 ◽  
Vol 16 (01) ◽  
pp. 17-22 ◽  
Author(s):  
Qaiser Mushtaq ◽  
Madad Khan
Keyword(s):  
Homomorphic Image ◽  
Equivalence Classes ◽  
Semilattice Decomposition

We consider a locally associative AG **-groupoid S and show that it has associative powers. We define ρ on S as aρb if and only if bna = bn+1 and anb = an+1 for all a, b ∈ S, and show that S/ρ is a maximal separative homomorphic image of S. We show that every S can be uniquely expressible as a semilattice Y of locally associative Archimedean AG **-groupoids Sα(α ∈ Y), the semilattice Y is isomorphic to a maximal homomorphic image S/η of S, and Sα(α ∈ Y) are the equivalence classes of S mod η.

scholarly journals On the structure of symmetric n-ary bands

2021 ◽  
pp. 1-20
Author(s):  
Jimmy Devillet ◽  
Pierre Mathonet
Keyword(s):  
Structure Theorem ◽  
Abelian Groups ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Semilattice Decomposition ◽  
Strong Semilattice ◽  
Necessary And Sufficient

We study the class of symmetric [Formula: see text]-ary bands. These are [Formula: see text]-ary semigroups [Formula: see text] such that [Formula: see text] is invariant under the action of permutations and idempotent, i.e., satisfies [Formula: see text] for all [Formula: see text]. We first provide a structure theorem for these symmetric [Formula: see text]-ary bands that extends the classical (strong) semilattice decomposition of certain classes of bands. We introduce the concept of strong [Formula: see text]-ary semilattice of [Formula: see text]-ary semigroups and we show that the symmetric [Formula: see text]-ary bands are exactly the strong [Formula: see text]-ary semilattices of [Formula: see text]-ary extensions of Abelian groups whose exponents divide [Formula: see text]. Finally, we use the structure theorem to obtain necessary and sufficient conditions for a symmetric [Formula: see text]-ary band to be reducible to a semigroup.

Subgroups of the Power Semigroup of a Finite Semigroup

1979 ◽  
Vol 31 (5) ◽  
pp. 1077-1083 ◽  
Author(s):  
Mohan S. Putcha
Keyword(s):  
Finite Semigroup ◽  
Normal Subgroups ◽  
Power Semigroup ◽  
Positive Integers

Throughout this paper, S will denote a finite semigroup and Z+ the set of positive integers. E = E(S) denotes the set of idempotents of S. Let . If , then let AB = {ab| a ∈ A, b ∈ B}. has been studied by many authors, including [2, 3, 5, 6, 7]. If X is a set, then |X| denotes the cardinality of X. For undefined terms in this paper, see [1,4].THEOREM 1. Let I be an ideal of S, a subgroup of . Then has a normal subgroups such that is isomorphic to a subgroup of and is isomorphic to a subgroup of .

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