A note on comaximal graph and maximal topology on multiplication le-modules

Ballal Sachin; Puranik Sadashiv; Kharat Vilas

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519.673 (7)

Matematică computațională. Analiză numerică. Programarea calculatoarelor (124)

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BALLAL, Sachin, PURANIK, Sadashiv, KHARAT, Vilas. A note on comaximal graph and maximal topology on multiplication le-modules. In: Quasigroups and Related Systems, 2023, vol. 31, nr. 2, pp. 175-184. ISSN 1561-2848. DOI: https://doi.org/10.56415/qrs.v31.13

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Quasigroups and Related Systems

Volumul 31, Numărul 2 / 2023 / ISSN 1561-2848

A note on comaximal graph and maximal topology on multiplication le-modules

DOI:https://doi.org/10.56415/qrs.v31.13

CZU: 519.673

MSC 2010: 06E10, 06E99, 06F99,06B23, 06F25

Pag. 175-184

Ballal Sachin¹, Puranik Sadashiv², Kharat Vilas²

¹ School of Mathematics and Statistics, University of Hyderabad,
² Savitribai Phule Pune University

Disponibil în IBN: 21 aprilie 2024

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In this article, the co-maximal graph ?(M) on le-modules M has been introduced and studied. The graph ?(M) consists of vertices as elements of RM and two distinct elements n;m of ?(M) are adjacent if and only if Rn + Rm = e. We have established a connection between the co-maximal graph and the maximal topology on Max(M) in the case of multiplication le-modules. Also, the Beck’s conjecture is settled for ?(M) which does not contain an infinite clique.

Cuvinte-cheie
Prime submodule element, radical element, Zariski topology, complete lattices, le-modules

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