Proceedings of the 2015 International Conference on Intelligent Systems Research and Mechatronics Engineering

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Definitions of BCK algebras and BCI algebras

Authors
Kun-Long Zhang, Li-xia Song
Corresponding Author
Kun-Long Zhang
Available Online April 2015.
DOI
10.2991/isrme-15.2015.226How to use a DOI?
Keywords
BCK algebra; BCI algebra; Algebra of type(2,0).
Abstract

In this paper, we consider the definitions of the BCK and BCI Algebra. We put out four examples in order to prove that any one of the four conditions in the definition of BCK algebra cannot be proofed by other three conditions. Next we simplify the definitions of the BCK and BCI Algebra by giving new equivalent conditions.

Copyright
© 2015, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Volume Title
Proceedings of the 2015 International Conference on Intelligent Systems Research and Mechatronics Engineering
Series
Advances in Intelligent Systems Research
Publication Date
April 2015
ISBN
10.2991/isrme-15.2015.226
ISSN
1951-6851
DOI
10.2991/isrme-15.2015.226How to use a DOI?
Copyright
© 2015, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - CONF
AU  - Kun-Long Zhang
AU  - Li-xia Song
PY  - 2015/04
DA  - 2015/04
TI  - Definitions of BCK algebras and BCI algebras
BT  - Proceedings of the 2015 International Conference on Intelligent Systems Research and Mechatronics Engineering
PB  - Atlantis Press
SP  - 1085
EP  - 1089
SN  - 1951-6851
UR  - https://doi.org/10.2991/isrme-15.2015.226
DO  - 10.2991/isrme-15.2015.226
ID  - Zhang2015/04
ER  -