Displaying similar documents to “Several Classes of BCK-algebras and their Properties”

Commutative Energetic Subsets of BCK-Algebras

Young Bae Jun, Eun Hwan Roh, Seok Zun Song (2016)

Bulletin of the Section of Logic

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The notions of a C-energetic subset and (anti) permeable C-value in BCK-algebras are introduced, and related properties are investigated. Conditions for an element t in [0, 1] to be an (anti) permeable C-value are provided. Also conditions for a subset to be a C-energetic subset are discussed. We decompose BCK-algebra by a partition which consists of a C-energetic subset and a commutative ideal.

BCI-algebras with Condition (S) and their Properties

Tao Sun, Junjie Zhao, Xiquan Liang (2008)

Formalized Mathematics

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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

Commutative directoids with sectional involutions

Ivan Chajda (2007)

Discussiones Mathematicae - General Algebra and Applications

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The concept of a commutative directoid was introduced by J. Ježek and R. Quackenbush in 1990. We complete this algebra with involutions in its sections and show that it can be converted into a certain implication algebra. Asking several additional conditions, we show whether this directoid is sectionally complemented or whether the section is an NMV-algebra.

Commutative directoids with sectionally antitone bijections

Ivan Chajda, Miroslav Kolařík, Sándor Radeleczki (2008)

Discussiones Mathematicae - General Algebra and Applications

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We study commutative directoids with a greatest element, which can be equipped with antitone bijections in every principal filter. These can be axiomatized as algebras with two binary operations satisfying four identities. A minimal subvariety of this variety is described.