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, the ideal structure of the Kauffman monoid is described in terms of the Jones monoid and a purely combinatorial numerical function with linearly ordered ideals.
Abstract: The generators of the Temperley-Lieb algebra generate a monoid with an appealing geometric representation. It has been much studied, notably by Louis Kauffman. Borisavljevic, Dosen, and Petric gave a complete proof of its abstract presentation by generators and relations, and suggested the name “Kauffman monoid”. We bring the theory of semigroups to the study of a certain finite homomorphic image of the Kauffman monoid. We show the homomorphic image (the Jones monoid) to be a combinatorial and regular *-semigroup with linearly ordered ideals. The Kauffman monoid is explicitly described in terms of the Jones monoid and a purely combinatorial numerical function. We use this to describe the ideal structure of the Kauffman monoid and two other of its homomorphic images.
62 citations
TL;DR: An effective criterion for determining whether a given language has dot-depth 2 is conjecture and the condition is shown to be necessary in general, and sufficient for languages over a two-letter alphabet.
61 citations
60 citations
TL;DR: In this paper, the authors established conditions under which (Tt)t≥0 is similar to a contraction semigroup, i.e., there exists an isomorphism S E B (H) such that (S-1 Tt S)t ≥ 0 is a contraction semiigroup.
Abstract: )t≥0 on a Hilbert space H, we establish conditions under which (Tt)t≥0 is similar to a contraction semigroup, i.e., there exists an isomorphism S E B (H) such that (S-1 Tt S)t≥0 is a contraction semigroup. In the case when the generator -A of (Tt)t≥0 is one-to-one, we obtain that (Tt)t≥0 is similar to a contraction semigroup if and only if A admits bounded imaginary powers. This characterizes one-to-one operators of type strictly less than π/2 on H which belong to BIP (H).
60 citations
TL;DR: In this paper, it was shown that a numerical semigroup is pseudo-symmetric if and only if its semigroup ring is a Kunz ring, where the Frobenius number is odd.
Abstract: Symmetric numerical semigroups are probably the numerical semigroups that have been most studied in the literature. The motivation and introduction of these semigroups is due mainly to Kunz, who in his manuscript [44] proves that a onedimensional analytically irreducible Noetherian local ring is Gorenstein if and only if its value semigroup is symmetric. Symmetric numerical semigroups always have odd Frobenius number. The translation of this concept for numerical semigroups with even Frobenius number motivates the definition of pseudo-symmetric numerical semigroups. In [5] it is shown that these semigroups also have their interpretation in one-dimensional local rings, since a numerical semigroup is pseudo-symmetric if and only if its semigroup ring is a Kunz ring.
59 citations