Affiliation:
1. Department of Mathematics, Chamran University, Ahvaz, Iran
Abstract
We determine entirely which Artinian rings have maximal subring. In particular, we show that an Artinian ring without maximal subring is integral over some finite subring and in particular that every Artinian ring which is uncountable or of characteristic zero has a maximal subring. We also determine when a finite direct product of rings has a maximal subring. Finally, we show that if a ring R has an Artinian maximal subring then R itself is Artinian.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Algebra and Number Theory
Cited by
15 articles.
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