# 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

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topTao 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

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

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