Fuzzy Prime Ideals of Pseudo- ŁBCK-algebras

Grzegorz Dymek; Andrzej Walendziak

doi:10.5666/kmj.2015.55.1.51

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Fuzzy Prime Ideals of Pseudo- ŁBCK-algebras

Grzegorz Dymek Andrzej Walendziak

Year: 2015 Journal: Kyungpook mathematical journal Vol: 55 (1)Pages: 51-62 Publisher: Kyungpook National University

DOI: 10.5666/kmj.2015.55.1.51

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Abstract

Pseudo-ŁBCK-algebras are commutative pseudo-BCK-algebras with relative cancellation property. In the paper, we introduce fuzzy prime ideals in pseudo-ŁBCK-algebras and investigate some of their properties. We also give various characterizations of prime ideals and fuzzy prime ideals. Moreover, we present conditions for a pseudo-ŁBCKalgebra to be a pseudo-ŁBCK-chain.

Keywords:

Mathematics Prime (order theory) Boolean prime ideal theorem Commutative property Fuzzy logic Associated prime Pure mathematics Algebra over a field Discrete mathematics Combinatorics Artificial intelligence Computer science

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Advanced Algebra and Logic

Physical Sciences → Computer Science → Computational Theory and Mathematics

Fuzzy and Soft Set Theory

Social Sciences → Decision Sciences → Management Science and Operations Research

Rough Sets and Fuzzy Logic

Physical Sciences → Computer Science → Computational Theory and Mathematics

Fuzzy Prime Ideals of Pseudo- ŁBCK-algebras

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