<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

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

Siedlce University of Natural Sciences and Humanities

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

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 some generalizations of BCI algebras and its applications

Published Online: Dec 31, 2020

Page range: 79 - 94

Received: Jun 25, 2019

Accepted: Oct 15, 2019

DOI: https://doi.org/10.2478/aupcsm-2020-0007

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

© 2020 Lidia Obojska et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

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

Published Online: Dec 31, 2020

Page range: 79 - 94

Received: Jun 25, 2019

Accepted: Oct 15, 2019

DOI: https://doi.org/10.2478/aupcsm-2020-0007

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

© 2020 Lidia Obojska et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

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