On branchwise implicative BCI-algebras.

Chaudhry, Muhammad Anwar

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On some classes of BCH-algebras.

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BCI-algebras with Condition (S) and their Properties

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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

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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...