Symmetric $ n $-derivations on prime ideals with applications

Shakir Ali; Amal S. Alali; Sharifah K. Said Husain; Vaishali Varshney; Shakir Ali; Amal S. Alali; Sharifah K. Said Husain; Vaishali Varshney

doi:10.3934/math.20231410

AIMS Mathematics

2023, Volume 8, Issue 11: 27573-27588. doi: 10.3934/math.20231410

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Research article

Symmetric $ n $-derivations on prime ideals with applications

1.
Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India
2.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O.Box-84428, Riyadh-11671, Saudi Arabia
3.
Laboratory Cryptography, Analysis and Structure, Institute for Mathematical Research & Department of Mathematics and Statistics, Faculty of Science, University Putra Malaysia, Malaysia
4.
Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India

Received: 01 July 2023 Revised: 21 August 2023 Accepted: 19 September 2023 Published: 28 September 2023
MSC : 16N60, 16R50, 16W25

Let $ \mathfrak{S} $ be a ring. The main objective of this paper is to analyze the structure of quotient rings, which are represented as $ \mathfrak{S}/\mathfrak{P} $, where $ \mathfrak{S} $ is an arbitrary ring and $ \mathfrak{P} $ is a prime ideal of $ \mathfrak{S} $. The paper aims to establish a link between the structure of these rings and the behaviour of traces of symmetric $ n $-derivations satisfying some algebraic identities involving prime ideals of an arbitrary ring $ \mathfrak{S} $. Moreover, as an application of the main result, we investigate the structure of the quotient ring $ \mathfrak{S}/\mathfrak{P} $ and traces of symmetric $ n $-derivations.
- derivation,
- prime ideal,
- prime ring,
- derivation,
- symmetric derivation,
- symmetric $ n $-derivation
Citation: Shakir Ali, Amal S. Alali, Sharifah K. Said Husain, Vaishali Varshney. Symmetric $ n $-derivations on prime ideals with applications[J]. AIMS Mathematics, 2023, 8(11): 27573-27588. doi: 10.3934/math.20231410

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Abstract

Let $ \mathfrak{S} $ be a ring. The main objective of this paper is to analyze the structure of quotient rings, which are represented as $ \mathfrak{S}/\mathfrak{P} $, where $ \mathfrak{S} $ is an arbitrary ring and $ \mathfrak{P} $ is a prime ideal of $ \mathfrak{S} $. The paper aims to establish a link between the structure of these rings and the behaviour of traces of symmetric $ n $-derivations satisfying some algebraic identities involving prime ideals of an arbitrary ring $ \mathfrak{S} $. Moreover, as an application of the main result, we investigate the structure of the quotient ring $ \mathfrak{S}/\mathfrak{P} $ and traces of symmetric $ n $-derivations.

References

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