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Mathematica Bohemica, Vol. 147, No. 3, pp. 359-368, 2022

Direct summands of Goldie extending elements in modular lattices

Rupal Shroff

Received November 29, 2020.   Published online August 17, 2021.
Abstract:  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.
Keywords:  modular lattice; direct summand; Goldie extending element
Classification MSC:  06B10, 06C05
DOI:  10.21136/MB.2021.0181-20
PDF available at:  Institute of Mathematics CAS   Digital Mathematics Library
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Affiliations:   Rupal Shroff, School of Mathematics and Statistics, MIT World Peace University, S. No. 124, Paud Road, Kothrud, Pune, Maharashtra 411038, India, e-mail: rupal.shroff@mitwpu.edu.in, rupal_shroff84@yahoo.co.in
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