Quasi-affine algebraic monoids.
An exact sequence of torsion-free abelian groups is quasi-balanced if the induced sequence is exact for all rank-1 torsion-free abelian groups . This paper sets forth the basic theory of quasi-balanced sequences, with particular attention given to the case in which is a Butler group. The special case where is almost completely decomposable gives rise to a descending chain of classes of Butler groups. This chain is a generalization of the chain of Kravchenko classes that arise from balanced...
The automorphisms of a quasigroup or Latin square are permutations of the set of entries of the square, and thus belong to conjugacy classes in symmetric groups. These conjugacy classes may be recognized as being annihilated by symmetric group class functions that belong to a -ideal of the special -ring of symmetric group class functions.
Let be a division groupoid that is not a quasigroup. For each regular cardinal we construct a quasigroup on that is a quasigroup cover of (i.e., is a homomorphic image of and is not an image of any quasigroup that is a proper factor of ). We also show how to easily obtain quasigroup covers from free quasigroups.
The aim of this paper is to prove that a quasigroup with right unit is isomorphic to an -extension of a right nuclear normal subgroup by the factor quasigroup if and only if there exists a normalized left transversal to in such that the right translations by elements of commute with all right translations by elements of the subgroup . Moreover, a loop is isomorphic to an -extension of a right nuclear normal subgroup by a loop if and only if is middle-nuclear, and there exists...