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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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The rings which are Boolean

100%
Chajda I., Švrček F.
Discussiones Mathematicae - General Algebra and Applications
|
2011
|
tom 31
|
nr 2
175-184
EN
We study unitary rings of characteristic 2 satisfying identity $x^p = x$ for some natural number p. We characterize several infinite families of these rings which are Boolean, i.e., every element is idempotent. For example, it is in the case if $p = 2^{n} - 2$ or $p = 2^{n} - 5$ or $p = 2^{n} + 1$ for a suitable natural number n. Some other (more general) cases are solved for p expressed in the form $2^{q} + 2m + 1$ or $2^{q} + 2m$ where q is a natural number and $m ∈ {1,2,...,2^{q} - 1}$.
3
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Ring-like operations is pseudocomplemented semilattices

75%
Chajda I., Länger H.
Discussiones Mathematicae - General Algebra and Applications
|
2000
|
tom 20
|
nr 1
87-95
EN
Ring-like operations are introduced in pseudocomplemented semilattices in such a way that in the case of Boolean pseudocomplemented semilattices one obtains the corresponding Boolean ring operations. Properties of these ring-like operations are derived and a characterization of Boolean pseudocomplemented semilattices in terms of these operations is given. Finally, ideals in the ring-like structures are defined and characterized.
4
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Some distributivities in GBbi-QRs characterizing Boolean rings

75%
Kaleta J.
Discussiones Mathematicae - General Algebra and Applications
|
2004
|
tom 24
|
nr 1
115-124
EN
This paper presents some manner of characterization of Boolean rings. These algebraic systems one can also characterize by means of some distributivities satisfied in GBbi-QRs.
5
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Representation of Hilbert algebras and implicative semilattices

63%
Celani S.
Open Mathematics
|
2003
|
tom 1
|
nr 4
561-572
EN
In this paper we shall give a topological representation for Hilbert algebras that extend the topological representation given by A. Diego in [4]. For implicative semilattices this representation gives a full duality. We shall also consider the representation for Boolean ring.
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