Abstract

We introduce and investigate the strong p-semisimple property for some generalizations of BCI algebras. For BCI algebras, the strong p-semisimple property is equivalent to the p-semisimple property. We describe the connections of strongly p-semisimple algebras and various generalizations of groups (such as, for example, involutive moons and goops). Moreover, we present some examples of proper strongly p-semisimple algebras.

Highlights

  • Iséki (1966) introduced BCI algebras as algebraic models of BCI-logic. Hu and Li (1983) defined BCH algebras, which are a generalization of BCI algebras

  • These algebras are a common generalization of BCH and BZ algebras

  • We describe the connections of strongly p-semisimple algebras and various generalizations of groups (such as, for example, involutive moons and goops, which were introduced by Iorgulescu (2018))

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Summary

Introduction

Iséki (1966) introduced BCI algebras as algebraic models of BCI-logic. Hu and Li (1983) defined BCH algebras, which are a generalization of BCI algebras. Hu and Li (1983) defined BCH algebras, which are a generalization of BCI algebras. The new class of algebras called BH algebras was introduced by Jun et al (1998). These algebras are a common generalization of BCH and BZ algebras ( a generalization of BCI algebras). Iorgulescu (2016) introduced new generalizations of BCI algebras such as aRM**, *aRM**, BCH** algebras, and many others. Lei and Xi (1985) defined p-semisimple BCI algebras and proved that p-semisimple BCI algebras are equivalent with abelian groups. We describe the connections of strongly p-semisimple algebras and various generalizations of groups (such as, for example, involutive moons and goops, which were introduced by Iorgulescu (2018)). We give some examples of proper strongly p-semisimple algebras

Generalizations of BCI algebras
Generalizations of groups
Examples of proper strongly p-semisimple algebras
Compliance with ethical standards

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