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arXiv · 2211.06297

Some examples of BL-algebras using commutative rings

Cristina Flaut·Dana Piciu
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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, $r\geq 2,$ and \ all BL-chains with $k$ elements, $k\geq 4.$

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Cristina Flaut, Dana Piciu. 2022-11-11. Some examples of BL-algebras using commutative rings. https://arxiv.org/abs/2211.06297

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