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Keywords:
idempotent and distributive groupoids and algebras; Mal'cev products of varieties of algebras; independent varieties
idempotent and distributive groupoids and algebras; Mal'cev products of varieties of algebras; independent varieties
Summary:
The paper investigates idempotent, reductive, and distributive groupoids, and more generally $\Omega$-algebras of any type including the structure of such groupoids as reducts. In particular, any such algebra can be built up from algebras with a left zero groupoid operation. It is also shown that any two varieties of left $k$-step reductive $\Omega$-algebras, and of right $n$-step reductive $\Omega$-algebras, are independent for any positive integers $k$ and $n$. This gives a structural description of algebras in the join of these two varieties.
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