English

Rings as the unions of proper subrings

Rings and Algebras 2010-01-25 v1

Abstract

We describe all possible ways how a ring can be expressed as the union of three of its proper subrings. This is an analogue for rings of a 1926 theorem of Scorza about groups. We then determine the minimal number of proper subrings of the simple matrix ring Mn(q)M_{n}(q) whose union is Mn(q)M_{n}(q).

Keywords

Cite

@article{arxiv.1001.3984,
  title  = {Rings as the unions of proper subrings},
  author = {Andrea Lucchini and Attila Maroti},
  journal= {arXiv preprint arXiv:1001.3984},
  year   = {2010}
}