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Ojective ideals in modular lattices

Shriram K. NimbhorkarRupal C. Shroff — 2015

Czechoslovak Mathematical Journal

The concept of an extending ideal in a modular lattice is introduced. A translation of module-theoretical concept of ojectivity (i.e. generalized relative injectivity) in the context of the lattice of ideals of a modular lattice is introduced. In a modular lattice satisfying a certain condition, a characterization is given for direct summands of an extending ideal to be mutually ojective. We define exchangeable decomposition and internal exchange property of an ideal in a modular lattice. It is...

Goldie extending elements in modular lattices

Shriram K. NimbhorkarRupal 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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