Generalized co-annihilator of BL-algebras

In BL-algebras we introduce the concept of generalized co-annihilators as a generalization of coannihilator and the set of the form x 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...

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Bibliographic Details
Published in:Open mathematics (Warsaw, Poland) Poland), 2015-10, Vol.13 (1)
Main Authors: Meng, Biao Long, Xin, Xiao Long
Format: Article
Language:English
Subjects:
Algebra
BL-algebras
Boolean algebra
Boolean algebras
Filter
Generalized co-annihilator
Involutory filter
Minimal prime filter
Prime filter
Quotients
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Summary:In BL-algebras we introduce the concept of generalized co-annihilators as a generalization of coannihilator and the set of the form x 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:
ISSN:2391-5455
2391-5455
DOI:10.1515/math-2015-0060