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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.

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...

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