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Weighted w -core inverses in rings

Liyun Wu, Huihui Zhu (2023)

Czechoslovak Mathematical Journal

Let R be a unital * -ring. For any a , s , t , v , w ∈ R we define the weighted w -core inverse and the weighted dual s -core inverse, extending the w -core inverse and the dual s -core inverse, respectively. An element a ∈ R has a weighted w -core inverse with the weight v if there exists some x ∈ R such that a w x v x = x , x v a w a = a and ( a w x ) * = a w x . Dually, an element a ∈ R has a weighted dual s -core inverse with the weight t if there exists some y ∈ R such that y t y s a = y , a s a t y = a and ( y s a ) * = y s a . Several characterizations of weighted w -core invertible and weighted dual s -core invertible...

Weil uniformities for frames

Jorge Picado (1995)

Commentationes Mathematicae Universitatis Carolinae

In pointfree topology, the notion of uniformity in the form of a system of covers was introduced by J. Isbell in [11], and later developed by A. Pultr in [14] and [15]. Another equivalent notion of locale uniformity was given by P. Fletcher and W. Hunsaker in [6], which they called “entourage uniformity”. The purpose of this paper is to formulate and investigate an alternative definition of entourage uniformity which is more likely to the Weil pointed entourage uniformity, since it is expressed...

Well-quasi-ordering Aronszajn lines

Carlos Martinez-Ranero (2011)

Fundamenta Mathematicae

We show that, assuming PFA, the class of all Aronszajn lines is well-quasi-ordered by embeddability.

When a line graph associated to annihilating-ideal graph of a lattice is planar or projective

Atossa Parsapour, Khadijeh Ahmad Javaheri (2018)

Czechoslovak Mathematical Journal

Let ( L , ∧ , ∨ ) be a finite lattice with a least element 0. 𝔸 G ( L ) is an annihilating-ideal graph of L in which the vertex set is the set of all nontrivial ideals of L , and two distinct vertices I and J are adjacent if and only if I ∧ J = 0 . We completely characterize all finite lattices L whose line graph associated to an annihilating-ideal graph, denoted by 𝔏 ( 𝔸 G ( L ) ) , is a planar or projective graph.

When does an AB5* module have finite hollow dimension?

Derya Keskin Tütüncü, Rachid Tribak, Patrick F. Smith (2011)

Colloquium Mathematicae

Using a lattice-theoretical approach we find characterizations of modules with finite uniform dimension and of modules with finite hollow dimension.

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

Ninghua Gao, Qingguo Li, Zhaowen Li (2016)

Open Mathematics

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...

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