Near-Rings and Partitioned Groups |
| |
Authors: | J D P Meldrum A P J van der Walt |
| |
Institution: | 1. Department of Mathematics and Statistics , University of Edinburgh , Edinburgh, UK meldrum.john@gmail.com;3. Department of Mathematics , University of Stellenbosch , Stellenbosch, South Africa |
| |
Abstract: | Over a commutative ring R with identity, free modules M with 2 distinguished submodules are studied. The category Rep2R of such objects M have the obvious morphisms between them, which are homomorphisms between .R-modules preserving the distinguished submodules. The endo-morphisms for each M constitute a subalgebra EndRM of the algebra EndRM and the readability of λ-generated R-algebras A as EndRM is considered for cardinals λ. Despite the fact that 4 is the minimal number of distinguished submodules for realizing any algebra over a field il, we are able to prove a similar result in Rep2R for many rings R including R = Z and algebras which are cotorsion-free. Several examples illustrate the boarder line of our main result. The main theorem is applied for constructing Butler groups in 11] |
| |
Keywords: | Ideals Near-rings Partitioned groups Structure |
|
|