General Theory of Quasi-Commutative BCI-algebras

• Autorzy: Tao Sun , Weibo Pan , Chenglong Wu , Xiquan Liang
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2008
• Tom: 16
• Numer: 3
• Strony: 253-258

Daty

wydano

2008-01-01

online

2009-03-20

Twórcy

autor

Tao Sun

• Qingdao University of Science and Technology, China

autor

Weibo Pan

• Qingdao University of Science and Technology, China

autor

Chenglong Wu

• Qingdao University of Science and Technology, China

autor

Xiquan Liang

• Qingdao University of Science and Technology, China

Bibliografia

• [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.

Identyfikatory

DOI

10.2478/v10037-008-0030-2