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, S2 whose 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|,|S 2|}. Moreover we consider amalgams of finite inverse semigroups respecting the J-order proving that the free product with amalgamation is completely semisimple and we also provide necessary and sufficient conditions for the R-classes to be finite. © 2010 World Scientific Publishing Company.

Bicyclic subsemigroups in amalgams of finite inverse semigroups

Rodaro E.
2010

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, S2 whose 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|,|S 2|}. Moreover we consider amalgams of finite inverse semigroups respecting the J-order proving that the free product with amalgamation is completely semisimple and we also provide necessary and sufficient conditions for the R-classes to be finite. © 2010 World Scientific Publishing Company.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11311/1141879
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