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Generalized co-annihilator of BL-algebras
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Abstract
In BL-algebras we introduce the concept of generalized co-annihilators as a generalization of coannihilator
and the set of the form x-1F 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:
Title: Generalized co-annihilator of BL-algebras
Description:
Abstract
In BL-algebras we introduce the concept of generalized co-annihilators as a generalization of coannihilator
and the set of the form x-1F 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:.
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