Periodic BCI-algebras and Subgroups of Adjoint Monoids of BCI-algebras

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1998 English Publisher:Springer Science and Business Media LLCJournal:Semigroup Forum, volume 57, pages 315-320 (issn: 0037-1912, eissn: 1432-2137,

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Authors: Huang, Wenping; Sun, Dajun;

doi: 10.1007/pl00005981

Periodic BCI-algebras and Subgroups of Adjoint Monoids of BCI-algebras

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Abstract

Let \((X,\cdot,0)\) be a BCI-algebra. The set \(M(X)\) of all finite compositions of right shifts \(\rho_{a}(x)=xa\) is a commutative monoid with the unit \(\rho_{0}\). It is proved that there is a bijection from p-semisimple closed ideals of a BCI-algebra \(X\) to subgroups of \(M(X)\).

Keywords

BCK-algebras, BCI-algebras, monoid of shifts, p-semisimple closed ideals, p-semisimple BCI-algebra, periodic BCI-algebra, pomonoid

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