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Article | Open Access

Prime Ideal, Semiprime Ideal, and Radical 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, we develop a systematic theory for the ideals of an L-ring L(μ, R). We introduce the concepts of a prime ideal, a semiprime ideal, and the radical of an ideal in an L-ring. The notion of a maximal ideal has been introduced and discussed in different studies. We prove several results pertaining to these notions which are versions of their counterparts in classical ring theory. Besides this, we prove that for a commutative ring R, the radical η of an ideal η in an L-ring L(μ, R) is an ideal of μ provided that η has sup-property.

Keywords

prime idealsemiprime idealradical of an idealL-subring

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Fuzzy Information and Engineering
Volume 15 Issue 4,
December 2023
Pages 313-323
DOI: 10.26599/FIE.2023.9270022
Cite this article:
Prajapati AS, Ajmal N, Jahan I. Prime Ideal, Semiprime Ideal, and Radical of an Ideal of an L-Subring. Fuzzy Information and Engineering, 2023, 15(4): 313-323. https://doi.org/10.26599/FIE.2023.9270022

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Received: 23 December 2022
Revised: 21 February 2023
Accepted: 26 March 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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