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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On antiflexible algebras


Author: David J. Rodabaugh
Journal: Trans. Amer. Math. Soc. 169 (1972), 219-235
MSC: Primary 17A30
DOI: https://doi.org/10.1090/S0002-9947-1972-0313336-7
MathSciNet review: 0313336
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Abstract: In this paper we begin a classification of simple and semisimple totally antiflexible algebras (finite-dimensional) over splitting fields of char. $ \ne 2,3$. For such an algebra $ A$, let $ P$ be the largest associative ideal in $ {A^ + }$ and let $ {N^ + }$ be the radical of $ P$. We determine all simple and semisimple totally antiflexible algebras in which $ N \cdot N = 0$. Defining $ A$ to be of type $ (m,n)$ if $ {N^ + }$ is nilpotent of class $ m$ with $ \dim A = n$, we then characterize all simple nodal totally anti-flexible algebras (over fields of char. $ \ne 2,3$) of types $ (n,n)$ and $ (n - 1,n)$ and give preliminary results for certain other types.


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DOI: https://doi.org/10.1090/S0002-9947-1972-0313336-7
Keywords: Simple algebras, antiflexible algebras
Article copyright: © Copyright 1972 American Mathematical Society