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 paper, affine semigroups having one Betti element are characterized and some relevant non-unique factorization invariants for these semigroup are computed for numerical semiggroups.
Abstract: We characterize affine semigroups having one Betti element and we compute some relevant non-unique factorization invariants for these semigroups As an example, we particularize our description to numerical semigroups
34 citations
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34 citations
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TL;DR: The structure of general left-right inverse semigroups has been investigated in this paper, where it is shown that the set of idempotents of an orthodox semigroup S satisfies xyxzx=xyzx if and only if S is isomorphic to a subdirect product of a left inverse semiigroup and a right inverse semigroup.
Abstract: An orthodox semigroup S is called a left [right] inverse semigroup if the set of idempotents of S satisfies the identity xyx=xy [xyx=yx] Bisimple left [right] inverse semigroups have been studied by Venkatesan [6] In this paper, we clarify the structure of general left [right] inverse semigroups Further, we also investigate the structure of orthodox semigroups whose idempotents satisfy the identity xyxzx=xyzx In particular, it is shown that the set of idempotents of an orthodox semigroup S satisfies xyxzx=xyzx if and only if S is isomorphic to a subdirect product of a left inverse semigroup and a right inverse semigroup
34 citations
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34 citations
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TL;DR: In this paper, it was shown that the semigroup of nonnegative integers is not uniformly k-repetive and that any finitely generated and uniformly 4repetitive semigroup is finite.
Abstract: Letk be an integer greater than 1 andS be a finitely generated semigroup. The following propositions are equivalent: 1) the semigroup of non negative integers is not uniformlyk-repetitive; 2) any finitely generated and uniformlyk-repetitive semigroup is finite. As a consequence we prove that any finitely generated and uniformly 4-repetitive semigroup is finite.
34 citations