March 7, 2024Open Access

On the Wedderburn decomposition of the total ring of quotients of certain Iwasawa algebras

Key Points

The Wedderburn decomposition reveals algebraic structure in the total ring of quotients.
Total ring of quotients of completed group ring is confirmed as semisimple.
Assessment of group rings is used to derive related algebraic properties and decompositions in Iwasawa contexts, leading to an intricate understanding of the structures involved in arithmetic geometry and number theory dynamics. The results contribute to the ongoing discourse in algebra and its applications in number theory.

Abstract

Let G H be the semidirect product of a finite group H and Zₚ. Let F/ Qₚ be a finite extension with ring of integers OF. Then the total ring of quotients QF (G) of the completed group ring O₅[ G] is a semisimple ring. We determine its Wedderburn decomposition by relating it to the Wedderburn decomposition of the group ring FH.

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Cite This Study

Ben Forrás (Thu,) studied this question.

synapsesocial.com/papers/68e7567db6db6435876cde53 https://doi.org/https://doi.org/10.48550/arxiv.2403.04663

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