We give a complexity dichotomy for the Quantified Constraint Satisfaction Problem QCSP(H) when H is reflexive tournament. It well-known that tournaments can be split into sequence of strongly connected components H_1,...,H_n so there exists an edge from every vertex H_i to H_j if and only i<j. prove has both its initial final component (possibly equal) size 1, then in NL otherwise NP-hard.

It has recently been shown that a minimal reversible nonsymmetric ring order 256 answering question originally posed in paper on taxonomy of 2-primal rings. In different work, questions rings having to do with this were also answered. work it is abelian reflexive nonsemicommutative 256, related left open these previous works. here [Formula: see text] such ring. This consequence the main result ...

In Almost Free Modules, Set-theoretic Methods, Eklof and Mekler [5, p. 455, Problem 12] raised the question about the existence of dual abelian groups G which are not isomorphic to Z ⊕G. Recall that G is a dual group if G ∼= D for some groupD withD = Hom (D,Z). The existence of such groups is not obvious because dual groups are subgroups of cartesian products Z and therefore have very many homo...