The Structure of Local Rings with Singleton Basis and Their Enumeration

Yousef Alkhamees and Sami Alabiad ()
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Yousef Alkhamees: Department of Mathematics, King Saud University, Riyadh 11451, Saudi Arabia
Sami Alabiad: Department of Mathematics, King Saud University, Riyadh 11451, Saudi Arabia

Mathematics, 2022, vol. 10, issue 21, 1-10

Abstract: 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.

Keywords: local rings; chain rings; isomorphism classes; Galois rings (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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