On annihilators in BL-algebras

• Autorzy: Yu Xi Zou , Xiao Long Xin , Peng Fei He
• Języki publikacji: EN

Abstrakty

EN

In the paper, we introduce the notion of annihilators in BL-algebras and investigate some related properties of them. We get that the ideal lattice (I(L), ⊆) is pseudo-complemented, and for any ideal I, its pseudo-complement is the annihilator I⊥ of I. Also, we define the An (L) to be the set of all annihilators of L, then we have that (An(L); ⋂,∧An(L),⊥,{0}, L) is a Boolean algebra. In addition, we introduce the annihilators of a nonempty subset X of L with respect to an ideal I and study some properties of them. As an application, we show that if I and J are ideals in a BL-algebra L, then [...] JI⊥$J_I^ \bot $ is the relative pseudo-complement of J with respect to I in the ideal lattice (I(L), ⊆). Moreover, we get some properties of the homomorphism image of annihilators, and also give the necessary and sufficient condition of the homomorphism image and the homomorphism pre-image of an annihilator to be an annihilator. Finally, we introduce the notion of α-ideal and give a notation E(I ). We show that (E(I(L)), ∧E, ∨E, E(0), E(L) is a pseudo-complemented lattice, a complete Brouwerian lattice and an algebraic lattice, when L is a BL-chain or a finite product of BL-chains.

Słowa kluczowe

EN

BL-algebra; MV-algebra; Ideal; Annihilator; Homomorphism

Kategorie tematyczne

• 08A72: Fuzzy algebraic structures
• 06B75: Generalizations of lattices

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2016
• Tom: 14
• Numer: 1
• Strony: 324-337

Daty

wydano

2016-01-01

otrzymano

2015-10-14

zaakceptowano

2016-04-28

online

2016-05-21

Twórcy

autor

Yu Xi Zou

• College of Mathematics, Northwest University, Xi’an, 710127, P.R.

autor

Xiao Long Xin

• College of Mathematics, Northwest University, Xi’an, 710127, P.R.

autor

Peng Fei He

• School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710119, P.R.

Identyfikatory

DOI

10.1515/math-2016-0029