Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A Wedderburn decomposition for certain generalized right alternative algebras


Author: Harry F. Smith
Journal: Proc. Amer. Math. Soc. 58 (1976), 1-7
MSC: Primary 17A30
MathSciNet review: 0419540
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Finite-dimensional nonassociative algebras are considered which satisfy certain subsets of the following identities: (1) $ (x,x,x) = 0$, (2) $ (wx,y,z) + (w,x,[y,z]) = w(x,y,z) + (w,y,z)x$, (3) $ (w,x \cdot y,z) = x \cdot (w,y,z) + y \cdot (w,x,z)$, (4) $ (x,y,z) + (y,z,x) + (z,x,y) = 0$. It is first observed that nil algebras satisfying (1) and (2) are solvable. The standard Wedderburn principal theorem is then established both for algebras satisfying (1), (2) and (3) and for algebras which satisfy (2) and (4). Throughout it is assumed that the base fields have characteristic different from 2 and 3.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 17A30

Retrieve articles in all journals with MSC: 17A30


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0419540-0
Keywords: Generalized right alternative algebra, solvable, generalized alternative algebra, generalized $ ( - 1,1)$ algebra, Wedderburn decomposition
Article copyright: © Copyright 1976 American Mathematical Society