Abstract: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.
Keywords: idempotent and distributive groupoids and algebras, Mal'cev products of varieties of algebras, independent varieties
AMS Subject Classification: 08A05, 03C05, 08C15