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Keywords:
modular lattice; direct summand; Goldie extending element
modular lattice; direct summand; Goldie extending element
Summary:
In this paper some results on direct summands of Goldie extending elements are studied in a modular 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 characterizations of decomposition of a Goldie extending element in a modular lattice are obtained.
References:
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