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1
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On annihilators in BL-algebras

100%
Zou Y. X., Xin X. L., Fei He P.
Open Mathematics
|
2016
|
tom 14
|
nr 1
324-337
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.
2
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Ideals in distributive posets

86%
Batueva C., Semenova M.
Open Mathematics
|
2011
|
tom 9
|
nr 6
1380-1388
EN
We prove that any ideal in a distributive (relative to a certain completion) poset is an intersection of prime ideals. Besides that, we give a characterization of n-normal meet semilattices with zero, thus generalizing a known result for lattices with zero.
3
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Some versions of limit and Dieudonné-type theorems with respect to filter convergence for (ℓ)-group-valued measures

72%
Boccuto A., Dimitriou X., Papanastassiou N.
Open Mathematics
|
2011
|
tom 9
|
nr 6
1298-1311
EN
Some limit and Dieudonné-type theorems in the setting of (ℓ)-groups with respect to filter convergence are proved, extending earlier results.
4
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On ideal equal convergence

58%
Filipów R., Staniszewski M.
Open Mathematics
|
2014
|
tom 12
|
nr 6
896-910
EN
We consider ideal equal convergence of a sequence of functions. This is a generalization of equal convergence introduced by Császár and Laczkovich [Császár Á., Laczkovich M., Discrete and equal convergence, Studia Sci. Math. Hungar., 1975, 10(3–4), 463–472]. Our definition of ideal equal convergence encompasses two different kinds of ideal equal convergence introduced in [Das P., Dutta S., Pal S.K., On and *-equal convergence and an Egoroff-type theorem, Mat. Vesnik, 2014, 66(2), 165–177]_and [Filipów R., Szuca P., Three kinds of convergence and the associated I-Baire classes, J. Math. Anal. Appl., 2012, 391(1), 1–9]. We also solve a few problems posed in the paper by Das, Dutta and Pal.
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