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1
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When doL-fuzzy ideals of a ring generate a distributive lattice?

100%
Gao N., Li Q., Li Z.
Open Mathematics
|
2016
|
tom 14
|
nr 1
531-542
EN
The notion of L-fuzzy extended ideals is introduced in a Boolean ring, and their essential properties are investigated. We also build the relation between an L-fuzzy ideal and the class of its L-fuzzy extended ideals. By defining an operator “⇝” between two arbitrary L-fuzzy ideals in terms of L-fuzzy extended ideals, the result that “the family of all L-fuzzy ideals in a Boolean ring is a complete Heyting algebra” is immediately obtained. Furthermore, the lattice structures of L-fuzzy extended ideals of an L-fuzzy ideal, L-fuzzy extended ideals relative to an L-fuzzy subset, L-fuzzy stable ideals relative to an L-fuzzy subset and their connections are studied in this paper.
2
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Classification lattices are geometric for complete atomistic lattices

76%
Mao H.
Open Mathematics
|
2017
|
tom 15
|
nr 1
959-973
EN
We characterize complete atomistic lattices whose classification lattices are geometric. This implies an proper solution to a problem raised by S. Radeleczki in 2002.
3
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Ideals in distributive posets

64%
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.
4
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The subalgebra lattice of a finite algebra

46%
Pióro K.
Open Mathematics
|
2014
|
tom 12
|
nr 7
1052-1108
EN
The aim of this paper is to characterize pairs (L, A), where L is a finite lattice and A a finite algebra, such that the subalgebra lattice of A is isomorphic to L. Next, necessary and sufficient conditions are found for pairs of finite algebras (of possibly distinct types) to have isomorphic subalgebra lattices. Both of these characterizations are particularly simple in the case of distributive subalgebra lattices. We do not restrict our attention to total algebras only, but we consider the more general case of partial algebras. Moreover, we use connections between algebras and hypergraphs to solve these problems.
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