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G -supplemented property in the lattices

Shahabaddin Ebrahimi Atani (2022)

Mathematica Bohemica

Let L be a lattice with the greatest element 1 . Following the concept of generalized small subfilter, we define g -supplemented filters and investigate the basic properties and possible structures of these filters.

Generators of existence varieties of regular rings and complemented Arguesian lattices

Christian Herrmann, Marina Semenova (2010)

Open Mathematics

We proved in an earlier work that any existence variety of regular algebras is generated by its simple unital Artinian members, while any existence variety of Arguesian sectionally complemented lattices is generated by its simple members of finite length. A characterization of the class of simple unital Artinian members [members of finite length, respectively] of such varieties is given in the present paper.

Goldie extending elements in modular lattices

Shriram K. Nimbhorkar, Rupal C. Shroff (2017)

Mathematica Bohemica

The concept of a Goldie extending module is generalized to a Goldie extending element in a lattice. An element a of a lattice L with 0 is said to be a Goldie extending element if and only if for every b ≤ a there exists a direct summand c of a such that b ∧ c is essential in both b and c . Some properties of such elements are obtained in the context of modular lattices. We give a necessary condition for the direct sum of Goldie extending elements to be Goldie extending. Some characterizations of a decomposition...

Graph automorphisms and cells of lattices

Ján Jakubík (2003)

Czechoslovak Mathematical Journal

In this paper we apply the notion of cell of a lattice for dealing with graph automorphisms of lattices (in connection with a problem proposed by G. Birkhoff).

Group-valued measures on coarse-grained quantum logics

Anna de Simone, Pavel Pták (2007)

Czechoslovak Mathematical Journal

In it was shown that a (real) signed measure on a cyclic coarse-grained quantum logic can be extended, as a signed measure, over the entire power algebra. Later () this result was re-proved (and further improved on) and, moreover, the non-negative measures were shown to allow for extensions as non-negative measures. In both cases the proof technique used was the technique of linear algebra. In this paper we further generalize the results cited by extending group-valued measures on cyclic coarse-grained...

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