General Theory of Quasi-Commutative BCI-algebras

Tao Sun; Weibo Pan; Chenglong Wu; Xiquan Liang

Formalized Mathematics (2008)

  • Volume: 16, Issue: 3, page 253-258
  • ISSN: 1426-2630

Abstract

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It is known that commutative BCK-algebras form a variety, but BCK-algebras do not [4]. Therefore H. Yutani introduced the notion of quasicommutative BCK-algebras. In this article we first present the notion and general theory of quasi-commutative BCI-algebras. Then we discuss the reduction of the type of quasi-commutative BCK-algebras and some special classes of quasicommutative BCI-algebras.

How to cite

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Tao Sun, et al. "General Theory of Quasi-Commutative BCI-algebras." Formalized Mathematics 16.3 (2008): 253-258. <http://eudml.org/doc/267520>.

@article{TaoSun2008,
abstract = {It is known that commutative BCK-algebras form a variety, but BCK-algebras do not [4]. Therefore H. Yutani introduced the notion of quasicommutative BCK-algebras. In this article we first present the notion and general theory of quasi-commutative BCI-algebras. Then we discuss the reduction of the type of quasi-commutative BCK-algebras and some special classes of quasicommutative BCI-algebras.},
author = {Tao Sun, Weibo Pan, Chenglong Wu, Xiquan Liang},
journal = {Formalized Mathematics},
language = {eng},
number = {3},
pages = {253-258},
title = {General Theory of Quasi-Commutative BCI-algebras},
url = {http://eudml.org/doc/267520},
volume = {16},
year = {2008},
}

TY - JOUR
AU - Tao Sun
AU - Weibo Pan
AU - Chenglong Wu
AU - Xiquan Liang
TI - General Theory of Quasi-Commutative BCI-algebras
JO - Formalized Mathematics
PY - 2008
VL - 16
IS - 3
SP - 253
EP - 258
AB - It is known that commutative BCK-algebras form a variety, but BCK-algebras do not [4]. Therefore H. Yutani introduced the notion of quasicommutative BCK-algebras. In this article we first present the notion and general theory of quasi-commutative BCI-algebras. Then we discuss the reduction of the type of quasi-commutative BCK-algebras and some special classes of quasicommutative BCI-algebras.
LA - eng
UR - http://eudml.org/doc/267520
ER -

References

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  1. [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. 
  2. [2] Yuzhong Ding. Several classes of BCI-algebras and their properties. Formalized Mathematics, 15(1):1-9, 2007. 
  3. [3] Yuzhong Ding and Zhiyong Pang. Congruences and quotient algebras of BCI-algebras. Formalized Mathematics, 15(4):175-180, 2007. 
  4. [4] Jie Meng and YoungLin Liu. An Introduction to BCI-algebras. Shaanxi Scientific and Technological Press, 2001. 
  5. [5] Tao Sun, Dahai Hu, and Xiquan Liang. Several classes of BCK-algebras and their properties. Formalized Mathematics, 15(4):237-242, 2007. 
  6. [6] Andrzej Trybulec and Agata Darmochwał. Boolean domains. Formalized Mathematics, 1(1):187-190, 1990. 
  7. [7] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 

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