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Normal cryptogroups with an associate subgroup

Mario Petrich (2013)

Czechoslovak Mathematical Journal

Let S be a semigroup. For a , x ∈ S such that a = a x a , we say that x is an associate of a . A subgroup G of S which contains exactly one associate of each element of S is called an associate subgroup of S . It induces a unary operation in an obvious way, and we speak of a unary semigroup satisfying three simple axioms. A normal cryptogroup S is a completely regular semigroup whose ℋ -relation is a congruence and S / ℋ is a normal band. Using the representation of S as a strong semilattice of Rees matrix semigroups,...

On permutability in semigroup varieties

Bedřich Pondělíček (1991)

Mathematica Bohemica

The paper contains characterizations of semigroup varieties whose semigroups with one generator (two generators) are permutable. Here all varieties of regular * -semigroups are described in which each semigroup with two generators is permutable.

On sandwich sets and congruences on regular semigroups

Mario Petrich (2006)

Czechoslovak Mathematical Journal

Let S be a regular semigroup and E ( S ) be the set of its idempotents. We call the sets S ( e , f ) f and e S ( e , f ) one-sided sandwich sets and characterize them abstractly where e , f ∈ E ( S ) . For a , a ' ∈ S such that a = a a ' a , a ' = a ' a a ' , we call S ( a ) = S ( a ' a , a a ' ) the sandwich set of a . We characterize regular semigroups S in which all S ( e , f ) (or all S ( a ) ) are right zero semigroups (respectively are trivial) in several ways including weak versions of compatibility of the natural order. For every a ∈ S , we also define E ( a ) as the set of all idempotets e such that, for any congruence ρ on...

On structure space of Γ -semigroups

S. Chattopadhyay, S. Kar (2008)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper we introduce the notion of the structure space of Γ -semigroups formed by the class of uniformly strongly prime ideals. We also study separation axioms and compactness property in this structure space.

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