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

Abstract

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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

How to cite

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Tao 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

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  5. [5] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990. 
  6. [6] Yuzhong Ding. Several classes of BCI-algebras and their properties. Formalized Mathematics, 15(1):1-9, 2007. 
  7. [7] Yuzhong Ding and Zhiyong Pang. Congruences and quotient algebras of BCI-algebras. Formalized Mathematics, 15(4):175-180, 2007. 
  8. [8] Jie Meng and YoungLin Liu. An Introduction to BCI-algebras. Shaanxi Scientific and Technological Press, 2001. 
  9. [9] Andrzej Trybulec. Semilattice operations on finite subsets. Formalized Mathematics, 1(2):369-376, 1990. 
  10. [10] Wojciech A. Trybulec. Binary operations on finite sequences. Formalized Mathematics, 1(5):979-981, 1990. 
  11. [11] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990. 
  12. [12] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 

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