We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
On Maximal Subrings of Commutative Rings.
- Authors
Azarang, A.; Karamzadeh, O. A. S.
- Abstract
A proper subring S of a ring R is said to be maximal if there is no subring of R properly between S and R. If R is a noetherian domain with |R| > 2ℵ0, then |(R)| ≤ |(R)|, where (R) is the set of maximal subrings of R. A useful criterion for the existence of maximal subrings in any ring R is also given. It is observed that if S is a maximal subring of a ring R, then S is artinian if and only if R is artinian and integral over S. Surprisingly, it is shown that any infinite direct product of rings has always maximal subrings. Finally, maximal subrings of zero-dimensional rings are also investigated.
- Subjects
MAXIMAL subgroups; COMMUTATIVE rings; SEMILOCAL rings; ARTIN rings; VON Neumann regular rings; NOETHERIAN rings
- Publication
Algebra Colloquium, 2012, Vol 19, p1125
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S1005386712000909