Some examples of BL-algebras using commutative rings

2022/11/11 by Cristina Flaut, Flaut, Cristina, Dana Piciu +1
Computer Science · #Advanced Algebra and Logic #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2211.06297

openalex publication_date 2022/11/11 · openalex created_date 2022/12/26 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to analize the structure of BL-algebras using commutative rings. From computational considerations, we are very interested in the finite case. We present new ways to generate finite BL-algebras using commutative rings and we give summarizing statistics. Furthermore, we investigated BL-rings, i.e., commutative rings whose the lattice of ideals can be equiped with a structure of BL-algebra. A new characterization for these rings and their connections to other classes of rings are established. Also, we give examples of finite BL-rings for which their lattice of ideals is not an MV-algebra and using these rings we construct BL-algebras with 2^r+1 elements, r≥ 2, and all BL-chains with k elements, k≥ 4.

Related

• BL-rings
• A non commutative generalization BL-rings
• Remarks regarding some Algebras of Logic
• Connections between commutative rings and some algebras of logic
• Some applications of finite BL-algebras