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Commutative Chain Rings with Index of Nilpotency 5 and Residue Field
by
Sami Alabiad
, Alhanouf Ali Alhomaidhi
, Nawal A. Alsarori
in
chain rings
/ coding over rings
/ isomorphism classes
/ local rings
2024
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Commutative Chain Rings with Index of Nilpotency 5 and Residue Field
by
Sami Alabiad
, Alhanouf Ali Alhomaidhi
, Nawal A. Alsarori
in
chain rings
/ coding over rings
/ isomorphism classes
/ local rings
2024
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Commutative Chain Rings with Index of Nilpotency 5 and Residue Field
Journal Article
Commutative Chain Rings with Index of Nilpotency 5 and Residue Field
2024
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Overview
This paper gives a thorough characterization of chain rings with index of nilpotency 5 and residue field F pm, where p represents a prime number, contributing valuable insights to the field of algebraic structures. It carefully identifies and categorizes the family of chain rings with these specifications, thereby enhancing the understanding of their properties and applications. In addition, the work offers a detailed enumeration of all chain rings containing p5m elements. The significance of finite chain rings is emphasized, particularly in their suitability for coding theory, which confirms their relevance in contemporary mathematical and engineering contexts.
Publisher
MDPI AG
Subject
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