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Generalized co-annihilator of BL-algebras

2015; De Gruyter Open; Volume: 13; Issue: 1 Linguagem: Inglês

10.1515/math-2015-0060

2391-5455

Biao Long Meng, Xiao Long Xin,

Fuzzy and Soft Set Theory

Abstract In BL-algebras we introduce the concept of generalized co-annihilators as a generalization of coannihilator and the set of the form x -1 F where F is a filter, and study basic properties of generalized co-annihilators. We also introduce the notion of involutory filters relative to a filter F and prove that the set of all involutory filters relative to a filter with respect to the suit operations is a complete Boolean lattice and BL-algebra. We use the technology of generalized co-annihilators to give characterizations of prime filters and minimal prime filters, respectively. In particular, we give a representation of co-annihilators in the quotient algebra of a BL-algebra L via a filter F by means of generalized co-annihilators relative to F in L: