Classification of the finite dimensional absolute valued algebras having a non-zero central idempotent or a one-sided unity

被引：12

作者：

Cuenca Mira, Jose Antonio ^{[2
]}

Darpo, Erik ^{[1
]}

Dieterich, Ernst ^{[1
]}

机构：

[1] Uppsala Univ, Inst Matemat, SE-75106 Uppsala, Sweden

[2] Univ Malaga, Fac Ciencias, Dept Algebra Geometria & Topol, Malaga 29080, Spain

来源：

BULLETIN DES SCIENCES MATHEMATIQUES | 2010年 / 134卷 / 03期

关键词：

Composition algebra; Absolute valued algebra; e-Quadratic algebra; Classification; Normal form;

D O I：

10.1016/j.bulsci.2009.03.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An absolute valued algebra is a non-zero real algebra that is equipped with a multiplicative norm. We classify all finite dimensional absolute valued algebras having a non-zero central idempotent or a one-sided unity, up to algebra isomorphism. This completes earlier results of Ramirez Alvarez and Rochdi which, in our self-contained presentation, are recovered from the wider context of composition k-algebras with an LR-bijective idempotent. (C) 2009 Elsevier Masson SAS. All rights reserved.

引用

页码：247 / 277

页数：31

共 8 条

[1] A CLASS OF FINITE RINGS HAVING ONE-SIDED ZERO DIVISORS
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CHINESE SCIENCE BULLETIN, 1991, 36 (06): : 449 - 453
[2] A CLASS OF FINITE RINGS HAVING ONE-SIDED ZERO DIVISORS
蒋滋梅
ChineseScienceBulletin, 1991, (06) : 449 - 453
[3] One-Sided Isotopes of Finite-Dimensional Algebras
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[4] THE STRUCTURE OF MINIMAL ONE-SIDED IDEALS OF A RING AND THE PRIMITIVE RINGS WITH NON-ZERO SOCLES
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[7] Classification of the finite-dimensional real division composition algebras having a non-Abelian derivation algebra
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JOURNAL OF ALGEBRA, 2016, 445 : 35 - 77
[8] For any finitely generated module M with non-zero rank over a commutative one-dimensional Noetherian local domain, we study a numerical invariant h(M) based on a partial trace ideal of M. We study its properties and explore relations between this invariant and the colength of the conductor. Finally we apply this to the universally finite module of differentials ΩR/k, where R is a complete k-algebra with k any perfect field, to study a long-standing conjecture due to R. W. Berger. © 2022 Elsevier Inc. All rights reserved.
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