# BCI-algebras with Condition (S) and their Properties

Tao Sun; Junjie Zhao; Xiquan Liang

Formalized Mathematics (2008)

- Volume: 16, Issue: 1, page 65-71
- ISSN: 1426-2630

## Access Full Article

top## Abstract

top## How to cite

topTao Sun, Junjie Zhao, and Xiquan Liang. "BCI-algebras with Condition (S) and their Properties." Formalized Mathematics 16.1 (2008): 65-71. <http://eudml.org/doc/267500>.

@article{TaoSun2008,

abstract = {In this article we will first investigate the elementary properties of BCI-algebras with condition (S), see [8]. And then we will discuss the three classes of algebras: commutative, positive-implicative and implicative BCK-algebras with condition (S).MML identifier: BCIALG 4, version: 7.8.09 4.97.1001},

author = {Tao Sun, Junjie Zhao, Xiquan Liang},

journal = {Formalized Mathematics},

language = {eng},

number = {1},

pages = {65-71},

title = {BCI-algebras with Condition (S) and their Properties},

url = {http://eudml.org/doc/267500},

volume = {16},

year = {2008},

}

TY - JOUR

AU - Tao Sun

AU - Junjie Zhao

AU - Xiquan Liang

TI - BCI-algebras with Condition (S) and their Properties

JO - Formalized Mathematics

PY - 2008

VL - 16

IS - 1

SP - 65

EP - 71

AB - In this article we will first investigate the elementary properties of BCI-algebras with condition (S), see [8]. And then we will discuss the three classes of algebras: commutative, positive-implicative and implicative BCK-algebras with condition (S).MML identifier: BCIALG 4, version: 7.8.09 4.97.1001

LA - eng

UR - http://eudml.org/doc/267500

ER -

## References

top- [1] Grzegorz Bancerek. Curried and uncurried functions. Formalized Mathematics, 1(3):537-541, 1990.
- [2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
- [3] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
- [4] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
- [5] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
- [6] Yuzhong Ding. Several classes of BCI-algebras and their properties. Formalized Mathematics, 15(1):1-9, 2007.
- [7] Yuzhong Ding and Zhiyong Pang. Congruences and quotient algebras of BCI-algebras. Formalized Mathematics, 15(4):175-180, 2007.
- [8] Jie Meng and YoungLin Liu. An Introduction to BCI-algebras. Shaanxi Scientific and Technological Press, 2001.
- [9] Andrzej Trybulec. Semilattice operations on finite subsets. Formalized Mathematics, 1(2):369-376, 1990.
- [10] Wojciech A. Trybulec. Binary operations on finite sequences. Formalized Mathematics, 1(5):979-981, 1990.
- [11] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
- [12] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.