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Let be a type of algebras. A valuation of terms of type is a function assigning to each term of type a value . For , an identity of type is said to be -normal (with respect to valuation ) if either or both and have value . Taking with respect to the usual depth valuation of terms gives the well-known property of normality of identities. A variety is called -normal (with respect to the valuation ) if all its identities are -normal. For any variety , there is a least...
We present a groupoid which can be converted into a Boolean algebra with respect to term operations. Also conversely, every Boolean algebra can be reached in this way.
In [7] and [8], two sets of regular identities without finite proper models were introduced. In this paper we show that deleting one identity from any of these sets, we obtain a set of regular identities whose models include all affine spaces over GF(p) for prime numbers p ≥ 5. Moreover, we prove that this set characterizes affine spaces over GF(5) in the sense that each proper model of these regular identities has at least 13 ternary term functions and the number 13 is attained if and only if the...
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