Geodesic
Direct summands of Goldie extending elements in modular lattices
Mathematica Bohemica, Tome 147 (2022) no. 3, pp. 359-368

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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.
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.
DOI : 10.21136/MB.2021.0181-20
Classification : 06B10, 06C05
Keywords: modular lattice; direct summand; Goldie extending element 
Shroff, Rupal. Direct summands of Goldie extending elements in modular lattices. Mathematica Bohemica, Tome 147 (2022) no. 3, pp. 359-368. doi: 10.21136/MB.2021.0181-20
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