Subsemivarieties of -algebras

Author:
M. H. Faroughi

Journal:
Proc. Amer. Math. Soc. **129** (2001), 1005-1014

MSC (1991):
Primary 46H99; Secondary 06B20

DOI:
https://doi.org/10.1090/S0002-9939-00-05641-0

Published electronically:
October 16, 2000

MathSciNet review:
1709750

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Abstract | References | Similar Articles | Additional Information

A variety is a class of Banach algebras , for which there exists a family of laws such that is precisely the class of all Banach algebras which satisfies all of the laws (i.e. for all , . We say that is an -variety if all of the laws are homogeneous. A semivariety is a class of Banach algebras , for which there exists a family of homogeneous laws such that is precisely the class of all Banach algebras , for which there exists such that for all homogeneous polynomials , , where . However, there is no variety between the variety of all -algebras and the variety of all -algebras, which can be defined by homogeneous laws alone. So the theory of semivarieties and the theory of varieties differ significantly. In this paper we shall construct uncountable chains and antichains of semivarieties which are not varieties.

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Additional Information

**M. H. Faroughi**

Affiliation:
Department of Pure Mathematics, University of Tabriz, Tabriz, Iran

Email:
mhfaroughi@ark.tabrizu.ac.ir

DOI:
https://doi.org/10.1090/S0002-9939-00-05641-0

Received by editor(s):
December 11, 1998

Received by editor(s) in revised form:
June 10, 1999

Published electronically:
October 16, 2000

Communicated by:
Dale Alspach

Article copyright:
© Copyright 2000
American Mathematical Society