Free nearrings
An explicit construction of a free nearring as well as the free product (= coproduct) of two nearrings are given in the variety of all, not necessarily zero-symmetric, nearrings.
math.RA↗
arXiv subjects
Stefan Veldsman
Publications and source records attributed to Stefan Veldsman.
An extension theory and semidirect sums for nearrings
An extension theory for nearrings along the lines of the Schreier extension for groups and the Everett extension for rings is given. The semidirect sum of two nearrings is a special case of this theory. Already there are many examples of purpose built nearring constructions in the theory of nearrings which fall under this semidirect sum construction.
math.RA↗
The significance of the contributions of congruences to the theory of connectednesses and disconnectednesses for topological spaces and graphs
This is a survey of some of the consequences of the recently introduced congruences on the theory of connectednesses (radical classes) and disconnectednesses (semisimple classes) of graphs and topological spaces. In particular, it is shown that the connectednesses and disconnectednesses can be obtained as Hoehnke radicals and a connectedness has a characterization in terms of congruences resembling the classical characterization of its algebraic counterpart using ideals for a radical class. But this approach has also shown that there are some unexpected differences and surprises: an ideal-hereditary Hoehnke radical of topological spaces or graphs need not be a Kurosh-Amitsur radical and in the category of graphs with no loops, non-trivial connectednesses and disconnectednesses exist, but all Hoehnke radicals degenerate.
math.GN↗