## Anna Romanowska

*On reductive and distributive algebras *

Comment.Math.Univ.Carolinae 40,4 (1999) 617-629. **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

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