Goldie extending elements in modular lattices
Mathematica Bohemica, Tome 142 (2017) no. 2, pp. 163-180.

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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 $b \leq a$ there exists a direct summand $c$ of $a$ such that $b \wedge c$ 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 of a Goldie extending element in such a lattice are given. The concepts of an $a$-injective and an $a$-ejective element are introduced in a lattice and their properties related to extending elements are discussed.
DOI : 10.21136/MB.2016.0049-14
Classification : 06B10, 06C05
Mots-clés : modular lattice; Goldie extending element 
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Nimbhorkar, Shriram K.; Shroff, Rupal C. Goldie extending elements in modular lattices. Mathematica Bohemica, Tome 142 (2017) no. 2, pp. 163-180. doi : 10.21136/MB.2016.0049-14. https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2016.0049-14/

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