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Equiprime Ideals and Equiprime Semimodules in Boolean Like Semirings

Bhagavathula Venkata Narayana Murthy*

Department of Mathematics, Maharaj Vijayaram Gajapathi Raj College of Engineering Chintalavalsa, Vizianagaram, Andhra Pradesh, India.

Periodicity:July - December'2022
DOI : https://doi.org/10.26634/jmat.11.2.18889

Abstract

In this paper, the concepts of equiprime ideals and equiprime semi-modules in Boolean like semirings (now onwards denote ℜ_B) are introduced and illustrated with examples. It is established that if Ҏ is the equiprime ℜ_B–Ideal of the ℜ_B –module Ń then (Ҏ: Ń) is equiprime ideal of ℜ_B. Also it is approved that if Ń is an equiprime ℜ_B–module then (0: Ń) is an equiprime ideal of ℜ_B. Also, an important characterization of the equiprime ideal of ℜ_B in the semimodule structure over ℜ_B is put forward. Using this result, it can be proved that ℜ_B is equiprime if there exists a faithful equiprime ℜ_B–module Ń. Finally, it is proved that if Ń is an equiprime ℜ_B–module and Ϯ is an invariant subgroup of ℜ_B such that Ϯ is not contained in (0: Ń), then Ń is an equiprime Ϯ–module.

Mathematics Subject Classification: 16Y30, 16Y80.

Keywords

Boolean Like Semiring, Semi-Module Over Boolean like Semiring, Equiprime Ideal and Equiprime Semi-Module.

How to Cite this Article?

Murthy, B. V. N. (2022). Equiprime Ideals and Equiprime Semimodules in Boolean Like Semirings. i-manager’s Journal on Mathematics, 11(2), 13-18. https://doi.org/10.26634/jmat.11.2.18889

References

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