On the adjoint semigroups of \(p\)-separable BCI-algebras. (English) Zbl 0928.06012

Huang, Wenping; Liu, Fang

Semigroup Forum 58, No. 3, 317-322 (1999).

The notion of a p-semisimple algebra was introduced by T. D. Lei and the reviewer [Math. Jap. 30, No. 4, 511-517 (1985; Zbl 0594.03047)]. For a BCI-algebra one may consider the largest p-semisimple subalgebra, but this subalgebra is usually not an ideal. If it is an ideal, then the BCI-algebra is called a p-separable BCI-algebra. In the paper under review the authors first show under which conditions this subalgebra forms an ideal and then they show that the adjoint semigroup of a p-separable algebra is closely related to negatively partially ordered semigroups and abelian groups.

Reviewer: Xi Changchang (Beijing)

MSC:

06F35	BCK-algebras, BCI-algebras
06F05	Ordered semigroups and monoids

Keywords:

p-semisimple BCI-algebra; p-separable BCI-algebra; partially ordered semigroup

Citations:

Zbl 0594.03047

References:

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