Maximal non-pseudovaluation subrings of an integral domain
Czechoslovak Mathematical Journal (2024)
- Volume: 74, Issue: 2, page 389-395
- ISSN: 0011-4642
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topKumar, Rahul. "Maximal non-pseudovaluation subrings of an integral domain." Czechoslovak Mathematical Journal 74.2 (2024): 389-395. <http://eudml.org/doc/299582>.
@article{Kumar2024,
abstract = {The notion of maximal non-pseudovaluation subring of an integral domain is introduced and studied. Let $R\subset S$ be an extension of domains. Then $R$ is called a maximal non-pseudovaluation subring of $S$ if $R$ is not a pseudovaluation subring of $S$, and for any ring $T$ such that $R \subset T\subset S$, $T$ is a pseudovaluation subring of $S$. We show that if $S$ is not local, then there no such $T$ exists between $R$ and $S$. We also characterize maximal non-pseudovaluation subrings of a local integral domain.},
author = {Kumar, Rahul},
journal = {Czechoslovak Mathematical Journal},
keywords = {maximal non-pseudovaluation domain; pseudovaluation subring},
language = {eng},
number = {2},
pages = {389-395},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Maximal non-pseudovaluation subrings of an integral domain},
url = {http://eudml.org/doc/299582},
volume = {74},
year = {2024},
}
TY - JOUR
AU - Kumar, Rahul
TI - Maximal non-pseudovaluation subrings of an integral domain
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 74
IS - 2
SP - 389
EP - 395
AB - The notion of maximal non-pseudovaluation subring of an integral domain is introduced and studied. Let $R\subset S$ be an extension of domains. Then $R$ is called a maximal non-pseudovaluation subring of $S$ if $R$ is not a pseudovaluation subring of $S$, and for any ring $T$ such that $R \subset T\subset S$, $T$ is a pseudovaluation subring of $S$. We show that if $S$ is not local, then there no such $T$ exists between $R$ and $S$. We also characterize maximal non-pseudovaluation subrings of a local integral domain.
LA - eng
KW - maximal non-pseudovaluation domain; pseudovaluation subring
UR - http://eudml.org/doc/299582
ER -
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