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## Open Mathematics

2016 | 14 | 1 | 324-337
Tytuł artykułu

### On annihilators in BL-algebras

Autorzy
Treść / Zawartość
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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.
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EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
324-337
Opis fizyczny
Daty
wydano
2016-01-01
otrzymano
2015-10-14
zaakceptowano
2016-04-28
online
2016-05-21
Twórcy
autor
• College of Mathematics, Northwest University, Xi’an, 710127, P.R.
autor
• College of Mathematics, Northwest University, Xi’an, 710127, P.R., xlxin@nwu.edu.cn
autor
• School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710119, P.R.
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