Open Access
On Maximal Subrings of Commutative Rings
Publication type: Journal Article
Publication date: 2012-10-31
scimago Q3
wos Q4
SJR: 0.325
CiteScore: 0.6
Impact factor: 0.4
ISSN: 10053867, 02191733
Applied Mathematics
Algebra and Number Theory
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 | Max (R)| ≤ | RgMax (R)|, where RgMax (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.
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16
Total citations:
16
Citations from 2024:
1
(6.25%)
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GOST
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AZARANG A., KARAMZADEH O. A. S. On Maximal Subrings of Commutative Rings // Algebra Colloquium. 2012. Vol. 19. No. spec01. pp. 1125-1138.
GOST all authors (up to 50)
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AZARANG A., KARAMZADEH O. A. S. On Maximal Subrings of Commutative Rings // Algebra Colloquium. 2012. Vol. 19. No. spec01. pp. 1125-1138.
Cite this
RIS
Copy
TY - JOUR
DO - 10.1142/S1005386712000909
UR - https://doi.org/10.1142/S1005386712000909
TI - On Maximal Subrings of Commutative Rings
T2 - Algebra Colloquium
AU - AZARANG, A.
AU - KARAMZADEH, O. A. S.
PY - 2012
DA - 2012/10/31
PB - World Scientific
SP - 1125-1138
IS - spec01
VL - 19
SN - 1005-3867
SN - 0219-1733
ER -
Cite this
BibTex (up to 50 authors)
Copy
@article{2012_AZARANG,
author = {A. AZARANG and O. A. S. KARAMZADEH},
title = {On Maximal Subrings of Commutative Rings},
journal = {Algebra Colloquium},
year = {2012},
volume = {19},
publisher = {World Scientific},
month = {oct},
url = {https://doi.org/10.1142/S1005386712000909},
number = {spec01},
pages = {1125--1138},
doi = {10.1142/S1005386712000909}
}
Cite this
MLA
Copy
AZARANG, A., and O. A. S. KARAMZADEH. “On Maximal Subrings of Commutative Rings.” Algebra Colloquium, vol. 19, no. spec01, Oct. 2012, pp. 1125-1138. https://doi.org/10.1142/S1005386712000909.
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