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Article | Open Access

Associated Prime Ideal and Minimal Prime Ideal of an Ideal of an L-Subring

Anand Swaroop Prajapati1, Naseem Ajmal2, Iffat Jahan3( )
Atma Ram Sanatan Dharma College, University of Delhi, New Delhi 110021, India
Zakir Husain College, University of Delhi, New Delhi 110006, India
Ramjas College, University of Delhi, New Delhi 110007, India
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Abstract

In this paper, a systematic theory for the ideals of an L-ring L(μ,R) has been developed. Earlier the authors have introduced the concepts of prime ideals, semiprime ideals, primary ideals, and radical of an ideal in an L-ring. They have also introduced and discussed the notion of a maximal ideal in different papers wherein several results pertaining to these notions have been proved. In this paper, the concepts of associated prime ideal, minimal prime ideal, and that of irreducibility of an ideal in an L-ring have been introduced, which in fact, are the continuation of authors’ previous works in the theory of ideals in L-rings.

Keywords

prime idealsemiprime idealprimary idealradical of an idealL-subring

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Fuzzy Information and Engineering
Volume 15 Issue 4,
December 2023
Pages 324-334
DOI: 10.26599/FIE.2023.9270023
Cite this article:
Prajapati AS, Ajmal N, Jahan I. Associated Prime Ideal and Minimal Prime Ideal of an Ideal of an L-Subring. Fuzzy Information and Engineering, 2023, 15(4): 324-334. https://doi.org/10.26599/FIE.2023.9270023

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Received: 19 April 2023
Revised: 21 August 2023
Accepted: 02 September 2023
Published: 02 January 2024
© The Author(s) 2023. Published by Tsinghua University Press.

This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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