Previous |  Up |  Next


idempotent and distributive groupoids and algebras; Mal'cev products of varieties of algebras; independent varieties
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.
[De] Dehornoy P.: Notes on Self-distributivity. preprint, Mathématiques, Université de Caen, France.
[Du] Dudek J.: On varieties of groupoid modes. Demonstratio Math. 27 (1994), 815-828. MR 1319426 | Zbl 0835.08003
[GLP] Grätzer G., Lakser H., Płonka J.: Joins and direct product of equational classes. Canad. Math. Bull. 12 (1969), 741-744. MR 0276160
[JKN] Ježek J., Kepka T., Němec P.: Distributive Groupoids. Academia Praha (1981). MR 0672563
[Kn] Knoebel A.: A product of independent algebras with finitely generated identities. Algebra Universalis 3 (1973), 147-151. MR 0349543
[M] Mal'cev A.I.: Multiplication of classes of algebraic systems (in Russian). Sibirsk. Mat. Zh. 8 (1967), 346-365. MR 0213276
[PiR] Pilitowska A., Romanowska A.: Reductive modes. Periodica Math. Hung. 36 (1998), 67-78. MR 1684506 | Zbl 0924.08001
[PłR] Płonka J., Romanowska A.: Semilattice sums. Universal Algebra and Quasigroups (eds. A. Romanowska, J.D.H. Smith), Heldermann Verlag, Berlin (1992), 123-158. MR 1191231
[PRR] Pilitowska A., Romanowska A., Roszkowska B.: Products of mode varieties and algebras of subalgebras. Math. Slovaca 46 (1996), 497-514. MR 1451038 | Zbl 0890.08003
[RS] Romanowska A., Smith J.D.H.: Modal Theory. Heldermann Verlag, Berlin, 1985. MR 0788695 | Zbl 0553.08001
[RT] Romanowska A., Traina S.: Algebraic quasi-orders and sums of algebras. Discuss. Math. Algebra Stochastic Methods 19 (1999), 239-263. MR 1709970 | Zbl 0949.08001
Partner of
EuDML logo