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2 1999

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Left-edge solid varieties of differential groupoids

Arworn Sr., Denecke K.

Demonstratio Mathematica

1999

Vol. 32, nr 1

1-11

An identity s=t is called a hyperidentity in a variety V if by substituting terms of appropriate arity for the operation symbols in s=t, one obtains an identity satisfied in V. Such substitutions are called hypersubstitutions. In the paper we consider hyperidentities and hypersubstitutions in the variety of differential groupoids, certain idempotent and medial groupoids. differential groupoids are modes as defined in [Rom-S;85]. We show that this variety and all its subvarieties are left-edge solid.

Hyperidentities and hypersubstitutions in the variety of symmetric, idempotent, entropic groupoids

Arworn Sr., Denecke K.

Demonstratio Mathematica

1999

Vol. 32, nr 4

677-686

In this paper we determine the structure of the groupoid of normal form hypersubstitutions with respect to the variety of symmetric, idempotent, entropic groupoids, describe the monoid of all proper hypersubstitutions, and ask which identities are satisfied as hyperidentities.