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, the structure of the semigroup tree and the regularities on the number of descendants of each node observed earlier by the first author are investigated and the question of what kind of chains appear in the tree and characterize the properties (like being (in)finite) thereof.
Abstract: In this paper we elaborate on the structure of the semigroup tree and the regularities on the number of descendants of each node observed earlier by the first author. These regularities admit two different types of behavior and in this work we investigate which of the two types takes place for some well-known classes of semigroups. Also we study the question of what kind of chains appear in the tree and characterize the properties (like being (in)finite) thereof. We conclude with some thoughts that show how this study of the semigroup tree may help in solving the conjecture of Fibonacci-like behavior of the number of semigroups with given genus.
40 citations
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TL;DR: In this article, the conditions générales d'utilisation (http://www.numdam.org/legal.cedram.php) of the agreement are discussed.
Abstract: © Université Bordeaux 1, 1991, tous droits réservés. L’accès aux archives de la revue « Journal de Théorie des Nombres de Bordeaux » (http://jtnb.cedram.org/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
39 citations
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TL;DR: A semigroup S (with zero) is called a right inverse semigroup if every (nonnull) principal left ideal of S has a unique idempotent generator as discussed by the authors.
39 citations
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TL;DR: In this article, it was shown that if R and T are isomorphic rings, then (R and T) and (T) are semigroups under composition, then they are not isomorphic.
Abstract: The family (R) of all endomorphisms of a ring R is a semigroup under composition. It follows easily that if R and T are isomorphic rings, then (R) and (T) are isomorphic semigroups. We devote ourselves here to the converse question: ‘If (R) and (T) are isomorphic, must R and T be isomorphic?’ As one might expect, the answer is, in general, negative. For example, the ring of integers has precisely two endomorphisms – the zero endomorphism and the identity automorphism. Since the same is true of the ring of rational numbers, the two endomorphism semigroups are isomorphic while the rings themselves are certainly not.
38 citations