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Semisimple radical classes of involution algebras

Published online by Cambridge University Press:  20 January 2009

N. V. Loi
N. V. Loi
Affiliation:
Mathematical Institute of the Hungarian Academy of SciencesBudapestV. Reáltanodau. 13-15H-1053, Hungary
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J. Wichman has asked about semisimple radical classes of involution algebras. In the present paper we describe the semisimple radical classes of involution algebras over a field K* with involution *. If K* is infinite, then there are only trivial semisimple radical classes. If K* is finite then these classes are subdirect closures of strongly hereditary finite sets of finite idempotent algebras. In proving this result we determine the structure of certain simple involution algebras. We prove that the variety of symmetric involution algebras over Z(2) does not have attainable identities, answering a problem posed by Gardner [2]. Most of the results are valid also for involution rings (over the integers).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 32 , Issue 1 , February 1989 , pp. 1 - 9
Copyright
Copyright © Edinburgh Mathematical Society 1989

References

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