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Bases for the k-normalizations of varieties of bands

Cheng V., Wismath S.

Demonstratio Mathematica

2007

Vol. 40, nr 4

775-787

The usual depth measurement on terms of a fixed type type r assigns to each term a non-negative integer called its depth. For k > l, an identity s ~ t of type r is said to be k-normal (with respect to the depth measurement) if either s = t or both s and t have depth > k. Taking k=1 gives the well-known property of normality of identities. A variety is called k-normal (with respect to the depth measurement) if all its identities are k-normal. For any variety V, there is a least k-normal variety Nk(V) containing V, the variety determined by the set of all k-normal identities of V. In this paper we produce for every subvariety V of the variety B of bands (idempotent semigroups) a finite equational basis for Nk(V), for k > 1.