Generalized co-annihilator of BL-algebras

• Autorzy: Biao Long Meng , Xiao Long Xin
• Języki publikacji: EN

Abstrakty

EN

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:

Słowa kluczowe

EN

BL-algebras; Boolean algebras; Filter; Prime filter; Minimal prime filter; Generalized co-annihilator; Involutory filter

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

otrzymano

2014-11-26

zaakceptowano

2015-09-15

online

2015-10-19

Twórcy

autor

Biao Long Meng

• Department of Mathematics, Northwest University, Xi’an, P.R.China and College of Science,
  Xi’an University of Science and Technology, Xi’an, P.R.China

autor

Xiao Long Xin

• [e-mail]
  Xiao Long Xin:

Bibliografia

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Identyfikatory

DOI

10.1515/math-2015-0060