Generalized co-annihilator of BL-algebras

Biao Long Meng; Xiao Long Xin

Open Mathematics (2015)

  • Volume: 13, Issue: 1
  • ISSN: 2391-5455

Abstract

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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:

How to cite

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Biao Long Meng, and Xiao Long Xin. "Generalized co-annihilator of BL-algebras." Open Mathematics 13.1 (2015): null. <http://eudml.org/doc/275972>.

@article{BiaoLongMeng2015,
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:},
author = {Biao Long Meng, Xiao Long Xin},
journal = {Open Mathematics},
keywords = {BL-algebras; Boolean algebras; Filter; Prime filter; Minimal prime filter; Generalized co-annihilator; Involutory filter},
language = {eng},
number = {1},
pages = {null},
title = {Generalized co-annihilator of BL-algebras},
url = {http://eudml.org/doc/275972},
volume = {13},
year = {2015},
}

TY - JOUR
AU - Biao Long Meng
AU - Xiao Long Xin
TI - Generalized co-annihilator of BL-algebras
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - null
AB - 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:
LA - eng
KW - BL-algebras; Boolean algebras; Filter; Prime filter; Minimal prime filter; Generalized co-annihilator; Involutory filter
UR - http://eudml.org/doc/275972
ER -

References

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