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A Class Of Algebras Without Unity Element

Published online by Cambridge University Press:  20 November 2018

R. M. Thrall
R. M. Thrall*
Affiliation:
University of Michigan
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1. Introduction. In a study of the commuting algebra of tensor space representations of the orthogonal group W. P. Brown encountered a class of algebras for which the existence of a unity element was equivalent to semisimplicity, but which were of interest whether or not semisimple. He gave these algebras the name generalized-total matrix algebras and proved (2) that each such algebra was characterized by three integers l, r, m and was isomorphic to the algebra of all square matrices of degree r + I + m which have zeros in the first l rows and in the last r columns.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 7 , 1955 , pp. 382 - 390
Copyright
Copyright © Canadian Mathematical Society 1955

References

1. Artin, E., Nesbitt, C. J., and Thrall, R. M., Rings with minimum condition (University of Michigan Press, 1944).Google Scholar
2. Brown, W. P., Generalized matrix algebras, Can. J. Math., 7 (1955), 188–190.Google Scholar
3. Jans, J. P., On the indecomposable representations of algebras. 2200-5-T Engineering Research Institute, University of Michigan.Google Scholar