Article
Version 1
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On Some Special Cases of K ¨othe’s Conjecture
Version 1
: Received: 29 August 2024 / Approved: 1 September 2024 / Online: 2 September 2024 (13:18:01 CEST)
How to cite: De, S. On Some Special Cases of K ¨othe’s Conjecture. Preprints 2024, 2024090039. https://doi.org/10.20944/preprints202409.0039.v1 De, S. On Some Special Cases of K ¨othe’s Conjecture. Preprints 2024, 2024090039. https://doi.org/10.20944/preprints202409.0039.v1
Abstract
The primary purpose of this research article is to study the famous K$\ddot{o}$the's Conjecture for the special cases - when a ring $\mathfrak{R}$ is commutative, and when $\mathfrak{R}$ is an Algebra over a field. Furthermore, some open problems involving tensor product of Algebras over a field has also been discussed extensively along with their proofs. Subsequently, an equivelent statement of K$\ddot{o}$the's problem in terms of algebra of matrices has been established.
Keywords
K$\ddot{o}$the Conjecture; Rings; Ideals; Nil Ideal; Jacobson Radical; Nilpotent; Noetherian Rings; Artinian Rings; Two-Sided Ideals; K$\ddot{o}$the Subsets; Commutative Rings; Matrix Rings; Polynomial Rings; Algebra; Tensor Product; Modules; Field Extension
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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