BICYCLIC SUBSEMIGROUPS IN AMALGAMS OF FINITE INVERSE SEMIGROUPS

Author:

RODARO EMANUELE1

Affiliation:

1. Politecnico di Milano, Department of Mathematics "F. Brioschi", Piazza Leonardo da Vinci, 32, 20133 Milano, Italy

Abstract

It is well known that an inverse semigroup is completely semisimple if and only if it does not contain a copy of the bicyclic semigroup. We characterize the amalgams [S1, S2; U] of two finite inverse semigroups S1, S2whose free product with amalgamation is completely semisimple and we show that checking whether the amalgamated free product of finite inverse semigroups contains a bicyclic subsemigroup is decidable by means of a polynomial time algorithm with respect to max {|S1|,|S2|}. Moreover we consider amalgams of finite inverse semigroups respecting the [Formula: see text]-order proving that the free product with amalgamation is completely semisimple and we also provide necessary and sufficient conditions for the [Formula: see text]-classes to be finite.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Cited by 9 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. An amalgam of inverse semigroups is embedded into an amalgam with a lower bounded core;International Journal of Algebra and Computation;2021-06-18

2. Some completely semisimple HNN-extensions of inverse semigroups;International Journal of Algebra and Computation;2019-10-18

3. Normal forms for semigroup amalgams;Israel Journal of Mathematics;2017-04

4. Context-freeness of the languages of Schützenberger automata of HNN-extensions of finite inverse semigroups;Publications de l'Institut Math?matique (Belgrade);2016

5. Decidability Versus Undecidability of the Word Problem in Amalgams of Inverse Semigroups;Semigroups, Algebras and Operator Theory;2015

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