On arithmetic of certain matrix algebras
type: Item
instance of: scholarly article
title: On arithmetic of certain matrix algebras
zbMATH Open document ID: 0868.11053
author: Hisaichi Midorikawa
published in: Proceedings of the Japan Academy. Series A
publication date: 1997-08-19T00:00:00Z
review text: The purpose of this paper is to develop the arithmetic of \(\mathbb{Z}(\zeta)\) and the ideal class semigroups \({\mathcal G}\), as done earlier in [\textit{C. G. Latimer} and \textit{C. C. MacDuffee}, Ann. Math., II. Ser. 34, 313-316 (1933; Zbl 0006.29002); \textit{H. Midorikawa} (preprint); \textit{O. Taussky}, Can. J. Math. 1, 300-302 (1949; Zbl 0045.15404)], and to introduce Dirichlet series in order to calculate \(|{\mathcal G}|\) as well. Besides definitions and statements of theorems, or so, there are no proofs. The theorems apparently connect \(\zeta\)-functions, \(L\)-functions, class-numbers, order of unit groups, discriminants etc.
Mathematics Subject Classification ID: 11R54
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 15B33
zbMATH DE Number: 799713
zbMATH Keywords: matrix algebras
zbMATH Keywords: regulator
zbMATH Keywords: ideal class semigroups
zbMATH Keywords: Dirichlet series
zbMATH Keywords: \(\zeta\)-functions
zbMATH Keywords: \(L\)-functions
zbMATH Keywords: unit groups
reviewed by: Robert W. van der Waall
MaRDI profile type: Publication
full work available at URL: pjaa.71.19
OpenAlex ID: W2071312971
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DOI: 10.3792/PJAA.71.19
description: scientific article; zbMATH DE number 799713