Displaying similar documents to “BCI-algebras with Condition (S) and their Properties”

Several Classes of BCK-algebras and their Properties

Tao Sun, Dahai Hu, Xiquan Liang (2007)

Formalized Mathematics

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In this article the general theory of Commutative BCK-algebras and BCI-algebras and several classes of BCK-algebras are given according to [2].

Several Classes of BCI-algebras and their Properties

Yuzhong Ding (2007)

Formalized Mathematics

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I have formalized the BCI-algebras closely following the book [6], sections 1.1 to 1.3, 1.6, 2.1 to 2.3, and 2.7. In this article the general theory of BCI-algebras and several classes of BCI-algebras are given. MML identifier: BCIALG 1, version: 7.8.04 4.81.962

General Theory of Quasi-Commutative BCI-algebras

Tao Sun, Weibo Pan, Chenglong Wu, Xiquan Liang (2008)

Formalized Mathematics

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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.

On B-algebras

J. Neggers, Hee Sik Kim (2002)

Matematički Vesnik

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States on basic algebras

Ivan Chajda, Helmut Länger (2017)

Mathematica Bohemica

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States on commutative basic algebras were considered in the literature as generalizations of states on MV-algebras. It was a natural question if states exist also on basic algebras which are not commutative. We answer this question in the positive and give several examples of such basic algebras and their states. We prove elementary properties of states on basic algebras. Moreover, we introduce the concept of a state-morphism and characterize it among states. For basic algebras which...