The p-semisimple property for some generalizations of BCI algebras and its applications

Lidia Obojska, Andrzej Walendziak

Abstract


This paper presents some generalizations of BCI algebras (the RM, tRM, *RM, RM**, *RM**, aRM**, *aRM**, BCH**, BZ, pre-BZ and pre-BCI algebras). We investigate the p-semisimple property for algebras mentioned above; give some examples and display various conditions equivalent to p-semisimplicity. Finally, we present a model of mereology without antisymmetry (NAM) which could represent a tRM algebra.

Keywords


RM/tRM/*RM/RM**/*aRM/BCI/BCH/BZ/pre-BZ/pre-BCI algebras; p-semisimplicity; mereology; antisymmetry

Mathematics Subject Classification (2010)


06F35; 03G25; 06A06

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