Publication:
MacWilliams extending conditions and quasi-Frobenius rings

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2205.01830v1.pdf(137.15 KB)
Date
2022-09-01
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Authors
Guil Asensio, Pedro Antonio ; Srivastava, Ashish K.
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Publisher
Elsevier
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Matemáticas
DOI
https://doi.org/10.1016/j.jalgebra.2022.05.005
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info:eu-repo/semantics/article
Description
© 2022 Elsevier Inc. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ This document is the Accepted Manuscript version of a Published Work that appeared in final form in Journal of Algebra. To access the final edited and published work see https://doi.org/10.1016/j.jalgebra.2022.05.005
Abstract
MacWilliams proved that every finite field has the extension property for Hamming weight which was later extended in a seminal work by Wood who characterized finite Frobenius rings as precisely those rings which satisfy the MacWilliams extension property. In this paper, the question of when is a MacWilliams ring quasi-Frobenius is addressed. It is proved that a right or left noetherian left 1-MacWilliams ring is quasi-Frobenius thus answering the different questions asked in [13], [22]. We also prove that a right perfect, left automorphism-invariant ring is left self-injective. In particular, this yields that if R is a right (or left) artinian, left automorphism-invariant ring, then R is quasi-Frobenius, thus answering a question asked in [13].
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MacWilliams ring , Quasi Frobenius ring , Automorphism invariant modules , Self injective rings , Perfect rings , Artinian rings
Citation
Journal of Algebra Vol. 2022, Vol. 605, pp. 394-402
URI
http://hdl.handle.net/10201/149027
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