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2016•Annals of the University of Craiova Mathematics and Computer Science SeriesRequires access

Integral ideals and maximal ideals in BL-algebras

Akbar Paad

Open publisher page 6 citations

Abstract

In this paper, we introduce the concept of integral ideals in BL-algebras. With respect to concept, we give some related results. In particular, we prove that an ideal is integral ideal if and only if is Boolean and (prime) maximal ideal. Also, we prove that a BL-algebra is an integral BL-algebra if and only if trivial ideal is an integral ideal. Moreover, we study relation between integral ideals and obstinate filters in BL-algebras by using the set of complement elements. Also, we describe relationship between maximal ideals in BL-algebras and locally finite MV-algebras.

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What this paper is about

In this paper, we introduce the concept of integral ideals in BL-algebras. With respect to concept, we give some related results. In particular, we prove that an ideal is integral ideal if and only if is Boolean and (prime) maximal ideal. Also, we prove that a BL-algebra is an integral BL-algebra if and only if trivial ideal is an integral ideal. Moreover, we study relation between integral ideals and obstinate filters in BL-algebras by using the set of complement elements. Also, we describe relationship between maximal ideals in BL-algebras and locally finite MV-algebras.

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Available abstract

In this paper, we introduce the concept of integral ideals in BL-algebras. With respect to concept, we give some related results. In particular, we prove that an ideal is integral ideal if and only if is Boolean and (prime) maximal ideal. Also, we prove that a BL-algebra is an integral BL-algebra if and only if trivial ideal is an integral ideal. Moreover, we study relation between integral ideals and obstinate filters in BL-algebras by using the set of complement elements. Also, we describe relationship between maximal ideals in BL-algebras and locally finite MV-algebras.

Key concepts: Mathematics, Boolean prime ideal theorem, Ideal (ethics), Fractional ideal, Maximal ideal, Minimal ideal, Radical of an ideal, Pure mathematics

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