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The Strong Condition on Inherently Nonfinitely Based Algebras
by
Zoltan Szekely
University of Guam
A finite algebra of finite type is inherently nonfinitely based provided it is not a member of any locally finite finitely based variety. A finite algebra A of finite type is said to be constantly bounded by the constant c if any finite algebra B is in the variety generated by A if and only if B satisfies those axioms of A that are no longer than c. It can be shown that if A is constantly bounded then it is either finitely based or inherently nonfinitely based. We say that A satisfies the strong condition on inherently nonfinitely based algebras if A is constantly bounded but not finitely based. We investigate the distinction between inherently nonfinitely based finite algebras and finite algebras with the strong condition on inherently nonfinitely based algebras (shortly finite algebras with the strong condition).
Date received: June 9, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caxi-33.