Subrings of Finite Commutative Rings
Francisco Franco Munoz
TL;DR
This paper investigates the structure of subrings within finite commutative rings, providing foundational results and specific calculations such as the number of maximal subrings in local rings.
Contribution
It introduces new theoretical results on subring structures and explicitly computes the count of maximal subrings in finite commutative local rings.
Findings
Established basic properties of subrings in finite commutative rings
Calculated the number of maximal subrings in finite commutative local rings
Provided applications related to ring theory
Abstract
We establish basic results on subrings of finite commutative rings and closely related rings. Among other applications we calculate the number of maximal subrings of a finite commutative local ring.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topics in Algebra · Finite Group Theory Research