Rings as the unions of proper subrings

Details Rings as the unions of proper subrings Rings as the unions of proper subrings

2010-01-22

arxiv.org/abs/1001.3984v1

Mathematics

Rings and Algebras

Scientific paper

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 $M_{n}(q)$ whose union is $M_{n}(q)$.

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