Prime Ideal, Semiprime Ideal, and Radical of an Ideal of an <i>L</i>-Subring

Anand Swaroop Prajapati; Naseem Ajmal; Iffat Jahan

doi:10.26599/FIE.2023.9270022

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Prime Ideal, Semiprime Ideal, and Radical of an Ideal of an L-Subring

Anand Swaroop Prajapati^¹, Naseem Ajmal^², Iffat Jahan^³()

1Atma Ram Sanatan Dharma College, University of Delhi, New Delhi 110021, India

2Zakir Husain College, University of Delhi, New Delhi 110006, India

3Ramjas 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 $\sqrt{η}$ of an ideal η in an L-ring L(μ, R) is an ideal of μ provided that η has sup-property.

Keywords

prime ideal semiprime ideal radical of an ideal L-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