MVLSC Home · Issue Contents · Forthcoming Papers
Some Results on Annihilator Complement in BL-Algebras
Javad Moghaderi, Somayeh Motamed and Arsham Borumand Saeid
In this paper, with the aim of further investigating on BL-algebras, we introduced the concept of the annihilator of complement elements of a non-empty subset X of a BL-algebra, (⊥(X−)), and we proved that this set is a filter. Then we examined and studied ⊥(X−) completely and showed under what conditions it becomes the prime and maximal filter. Next, with the help of ⊥(X−), we obtained an equivalence condition for fantastic filters, and since fantastic filters are directly related to MV-algebras, we were able to find an equivalence condition for checking MV-algebras. Also, we studied ⊥(X−) in various types of BL-algebras, including linearly ordered BL-algebras, Boolean algebra, Gödel algebra, integral and special BL-algebras. In the last part of this article, with the help of the spectrum of fantastic filters, (FS(L)), we introduced a new BL-algebra and examined some of its features.
Keywords: BL-algebra, MV-algebra, (fantastic, prime, maximal) filter
2020 Mathematics Subject Classification: Primary: 03B47; Secondary: 03G25, 06D35, 06D99.