M-solid varieties generated by lattices |
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| Authors: | P Penner SL Wismath R Padmanabhan |
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| Institution: | (1) University of Manitoba, Department of Mathematics, Winnipeg, Man. R3T 2N2, Canada, e-mail: ppenner@cc.umanitoba.ca, CA;(2) Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, Alberta, T1K 3M4, Canada, e-mail: wismaths@cs.uleth.ca, CA;(3) University of Manitoba, Department of Mathematics, Winnipeg, Man. R3T 2N2, Canada, e-mail: padman@cc.umanitoba.ca, CA |
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| Abstract: | Following W. Taylor, we define an identity to be hypersatisfied by a variety V iff, whenever the operation symbols of V are replaced by arbitrary terms (of appropriate arity) in the operations of V, then the resulting identity is satisfied by V in the usual sense. Whenever the identity is hypersatisfied by a variety V, we shall say that is a hyperidentity of
V, or a V
hyperidentity. When the terms being substituted are restricted to a submonoid M of all the possible choices, is called an M-hyperidentity, and a variety V is M-solid if each identity is an M-hyperidentity. In this paper we examine the solid varieties whose identities are lattice M-hyperidentities.
The M-solid varieties generated by the variety of lattices in this way provide new insight on the construction and representation
of various known classes of non-commutative lattices.
Received October 8, 1999; accepted in final form March 22, 2000. |
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| Keywords: | : Hyperidentity solid varieties lattices M-solid varieties |
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