Topic
Bicyclic semigroup
About: Bicyclic semigroup is a research topic. Over the lifetime, 1507 publications have been published within this topic receiving 19311 citations.
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TL;DR: In this article, it was proved that every semigroup from C is an absolute coretract and every finite semigroup of idempotents, which is a decreasing chain of rectangular semigroups, belongs to C.
Abstract: A semigroup S is called an absolute coretract if for any continuous homomorphism f from a compact Hausdorff right topological semigroup T onto a compact Hausdorff right topological semigroup containing S algebraically there exists a homomorphism g \colon S→ T such that f\circ g=idS. The semigroup β\ben contains isomorphic copies of any countable absolute coretract. In this article we define a class C of semigroups of idempotents each of which is a decreasing chain of rectangular semigroups. It is proved that every semigroup from C is an absolute coretract and every finite semigroup of idempotents, which is an absolute coretract, belongs to C .
11 citations
TL;DR: The topological finiteness condition finite derivation type (FDT) on the class of semigroups is introduced and it is proved that if a Rees matrix semigroup M has F DT then the semigroup S also has FDT.
11 citations
TL;DR: In this article, it was shown that for every finite weakly left ample semigroup S, there is a finite proper (2, 1)-subalgebra of S and an onto morphism from S to S which separates idempotents.
Abstract: Weakly left ample semigroups are a class of semigroups that are (2,1)-subalgebras of semigroups of partial transformations, where the unary operation takes a transformation α to the identity map in the domain of α It is known that there is a class of proper weakly left ample semigroups whose structure is determined by unipotent monoids acting on semilattices or categories In this paper we show that for every finite weakly left ample semigroup S, there is a finite proper weakly left ample semigroup Ŝ and an onto morphism from Ŝ to S which separates idempotents In fact, Ŝ is actually a (2,1)-subalgebra of a symmetric inverse semigroup, that is, it is a left ample semigroup (formerly, left type A)
11 citations
TL;DR: In this paper, it was shown that the semigroup generated by four binary relations contains all regular binary relations, which is the same as the regular binary semigroup of the binary relation.
Abstract: We prove the semigroup generated by four binary relations contains all regular binary relations.
11 citations
TL;DR: In this paper, the factor power of a transformation semigroup (S, M) is assigned to a semigroupFP(S) called the factor-power of the semigroup S, M, and applied to the symmetric group Sn.
Abstract: To a transformation semigroup (S, M) we assign a new semigroupFP(S) called the factor-power of the semigroup (S, M). Then we apply this construction to the symmetric groupSn. Some combinatorial properties of the semigroupFP(Sn) are studied; in particular, we investigate its relationship with the semigroup of 2-stochastic matrices of ordern and the structure of its idempotents. The idempotents are used in characterizingFP(Sn) as an extremal subsemigroup of the semigroupBn of all binary relations of ann-element set and also in the proof of the fact thatFP(Sn) contains almost all elements ofBn.
11 citations