Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

Open Access
Online
ISSN
1898-9934
See all formats and pricing
More options …
Volume 16, Issue 3 (Jan 2008)

Issues

General Theory of Quasi-Commutative BCI-algebras

Tao Sun
  • Qingdao University of Science and Technology, China
/ Weibo Pan
  • Qingdao University of Science and Technology, China
/ Chenglong Wu
  • Qingdao University of Science and Technology, China
/ Xiquan Liang
  • Qingdao University of Science and Technology, China
Published Online: 2009-03-20 | DOI: https://doi.org/10.2478/v10037-008-0030-2

General Theory of Quasi-Commutative BCI-algebras

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.

  • [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Google Scholar

  • [2] Yuzhong Ding. Several classes of BCI-algebras and their properties. Formalized Mathematics, 15(1):1-9, 2007.Google Scholar

  • [3] Yuzhong Ding and Zhiyong Pang. Congruences and quotient algebras of BCI-algebras. Formalized Mathematics, 15(4):175-180, 2007.Google Scholar

  • [4] Jie Meng and YoungLin Liu. An Introduction to BCI-algebras. Shaanxi Scientific and Technological Press, 2001.Google Scholar

  • [5] Tao Sun, Dahai Hu, and Xiquan Liang. Several classes of BCK-algebras and their properties. Formalized Mathematics, 15(4):237-242, 2007.Google Scholar

  • [6] Andrzej Trybulec and Agata Darmochwał. Boolean domains. Formalized Mathematics, 1(1):187-190, 1990.Google Scholar

  • [7] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Google Scholar

About the article


Published Online: 2009-03-20

Published in Print: 2008-01-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-008-0030-2.

Export Citation

This content is open access.

Comments (0)

Please log in or register to comment.
Log in