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The Structure of Local Rings with Singleton Basis and Their Enumeration
by
Alkhamees, Yousef
, Alabiad, Sami
in
Algebra
/ chain rings
/ Enumeration
/ Galois rings
/ Invariants
/ Isomorphism
/ isomorphism classes
/ local rings
/ Polynomials
/ Rings (mathematics)
2022
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The Structure of Local Rings with Singleton Basis and Their Enumeration
by
Alkhamees, Yousef
, Alabiad, Sami
in
Algebra
/ chain rings
/ Enumeration
/ Galois rings
/ Invariants
/ Isomorphism
/ isomorphism classes
/ local rings
/ Polynomials
/ Rings (mathematics)
2022
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The Structure of Local Rings with Singleton Basis and Their Enumeration
Journal Article
The Structure of Local Rings with Singleton Basis and Their Enumeration
2022
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Overview
A local ring is an associative ring with unique maximal ideal. We associate with each Artinian local ring with singleton basis four invariants (positive integers) p,n,s,t. The purpose of this article is to describe the structure of such rings and classify them (up to isomorphism) with the same invariants. Every local ring with singleton basis can be constructed over its coefficient subring by a certain polynomial called the associated polynomial. These polynomials play significant role in the enumeration.
Publisher
MDPI AG
Subject
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