Semi-algebraic Absolute Valued Algebras with an Involution

Let A be an absolute valued algebra. In El-Mallah (El-Mallah,M. L. (1988). Absolute valued algebras with an involution. Arch. Math. 51: 39-49) we proved that,if A is algebraic with an involution,then A is finite dimensional. This result had been generalized in El-Amin et al. (El-Amin,K.,Ramirez,M. I...

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Bibliographic Details
Published in:Communications in algebra 2003-01, Vol.31 (7), p.3135-3141
Main Author: El-Mallah, Mohamed Lamei
Format: Article
Language:English
Subjects:
Absolute valued
Algebra
Involution
Semi-algebraic
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Summary:Let A be an absolute valued algebra. In El-Mallah (El-Mallah,M. L. (1988). Absolute valued algebras with an involution. Arch. Math. 51: 39-49) we proved that,if A is algebraic with an involution,then A is finite dimensional. This result had been generalized in El-Amin et al. (El-Amin,K.,Ramirez,M. I.,Rodriguez,A. (1997). Absolute valued algebraic algebras are finite dimensional. J. Algebra 195:295-307),by showing that the condition "algebraic" is sufficient for A to be finite dimensional. In the present paper we give a generalization of the concept "algebraic",which will be called "semi-algebraic",and prove that if A is semi-algebraic with an involution then A is finite dimensional. We give an example of an absolute valued algebra which is semi-algebraic and infinite dimensional. This example shows that the assumption "with an involution" cannot be removed in our result.
ISSN:0092-7872
1532-4125
DOI:10.1081/AGB-120022215