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)



Two finitely generated varieties
having no infinite simple members

Author: Ross Willard
Journal: Proc. Amer. Math. Soc. 126 (1998), 629-635
MSC (1991): Primary 08B26
MathSciNet review: 1458270
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Using a method of R. McKenzie, we construct a finitely generated semisimple variety of infinite type, and a finitely generated nonsemisimple variety of finite type, both having arbitrarily large finite but no infinite simple members. This amplifies M. Valeriote's negative solution to Problem 11 from Hobby and McKenzie, The Structure of Finite Algebras.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 08B26

Retrieve articles in all journals with MSC (1991): 08B26

Additional Information

Ross Willard
Affiliation: Department of Pure Mathematics University of Waterloo Waterloo, Ontario, Canada N2L 3G1

Keywords: Variety, finitely generated, simple, semisimple
Received by editor(s): October 26, 1995
Additional Notes: The support of the NSERC of Canada is gratefully acknowledged.
Communicated by: Lance W. Small
Article copyright: © Copyright 1998 American Mathematical Society