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

Lidia Obojska; Andrzej Walendziak

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica (2020)

  • Volume: 19, page 79-94
  • ISSN: 2300-133X

Abstract

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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.

How to cite

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Lidia Obojska, and Andrzej Walendziak. "The p-semisimple property for some generalizations of BCI algebras and its applications." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 19 (2020): 79-94. <http://eudml.org/doc/296822>.

@article{LidiaObojska2020,
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.},
author = {Lidia Obojska, Andrzej Walendziak},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
keywords = {RM/tRM/*RM/RM**/*aRM/BCI/BCH/BZ/pre-BZ/pre-BCI algebras; p-semisimplicity; mereology; antisymmetry},
language = {eng},
pages = {79-94},
title = {The p-semisimple property for some generalizations of BCI algebras and its applications},
url = {http://eudml.org/doc/296822},
volume = {19},
year = {2020},
}

TY - JOUR
AU - Lidia Obojska
AU - Andrzej Walendziak
TI - The p-semisimple property for some generalizations of BCI algebras and its applications
JO - Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
PY - 2020
VL - 19
SP - 79
EP - 94
AB - 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.
LA - eng
KW - RM/tRM/*RM/RM**/*aRM/BCI/BCH/BZ/pre-BZ/pre-BCI algebras; p-semisimplicity; mereology; antisymmetry
UR - http://eudml.org/doc/296822
ER -

References

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