Φ − X - Elements in Multiplicative Lattices

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Authors

  • Sachin Sarode
     Department of Mathematics, Shri Muktanand College, Gangapur. Dist. Aurangabad-431109, Maharashtra ,IN

DOI:

https://doi.org/10.18311/jims/2024/31309

Keywords:

Multiplicative lattice, Prime element, ϕ − X-element, ϕ − n-element, ϕ − J-element, ϕ − r-element, ϕ − n-ideal, ϕ − r-ideal, ϕ − J-ideal.

Abstract

In this paper, author presents a generalization of an X-element in a multiplicative lattice L. For a particular M-closed subset X, author defines the concept of ϕ − r-element, ϕ − n-element, and ϕ − J-element. These elements generalize the notion of ϕ − r-ideals, ϕ − n-ideals, and ϕ − J-ideals of a commutative ring with unity to multiplicative lattices. An ideal I of a commutative ring R with unity is a ϕ − n-ideal (ϕ − Jideal) of R if and only if I is a ϕ − n-element (ϕ − J-element) of Id(R), the ideal lattice of R is proved.

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Published

2024-01-01

How to Cite

Sarode, S. (2024). Φ − X - Elements in Multiplicative Lattices. The Journal of the Indian Mathematical Society, 91(1-2), 217–228. https://doi.org/10.18311/jims/2024/31309

Issue

Volume 91, Issue 1-2, January-June 2024

Section

Articles

License

Copyright (c) 2024 Sachin Sarode

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Europe PMC
Received 2022-09-22
Accepted 2023-09-20
Published 2024-01-01

 

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