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BCI-algebras with Condition (S) and their Properties

Tao SunJunjie ZhaoXiquan Liang — 2008

Formalized Mathematics

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

General Theory of Quasi-Commutative BCI-algebras

Tao SunWeibo PanChenglong WuXiquan Liang — 2008

Formalized Mathematics

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.

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