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Displaying similar documents to “Good and very good magnifiers”

Generalized F -semigroups

E. Giraldes, P. Marques-Smith, Heinz Mitsch (2005)

Mathematica Bohemica

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A semigroup S is called a generalized F -semigroup if there exists a group congruence on S such that the identity class contains a greatest element with respect to the natural partial order ≤ S of S . Using the concept of an anticone, all partially ordered groups which are epimorphic images of a semigroup ( S , · , ≤ S ) are determined. It is shown that a semigroup S is a generalized F -semigroup if and only if S contains an anticone, which is a principal order ideal of ( S , ≤ S ) . Also a characterization by means...

Characterizing pure, cryptic and Clifford inverse semigroups

Mario Petrich (2014)

Czechoslovak Mathematical Journal

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An inverse semigroup S is pure if e = e 2 , a ∈ S , e < a implies a 2 = a ; it is cryptic if Green’s relation ℋ on S is a congruence; it is a Clifford semigroup if it is a semillatice of groups. We characterize the pure ones by the absence of certain subsemigroups and a homomorphism from a concrete semigroup, and determine minimal nonpure varieties. Next we characterize the cryptic ones in terms of their group elements and also by a homomorphism of a semigroup constructed in the paper. We also characterize...

Normal cryptogroups with an associate subgroup

Mario Petrich (2013)

Czechoslovak Mathematical Journal

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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...