On domains with ACC on invertible ideals
- Volume: 82, Issue: 3, page 419-422
- ISSN: 1120-6330
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topGabelli, Stefania. "On domains with ACC on invertible ideals." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 82.3 (1988): 419-422. <http://eudml.org/doc/287370>.
@article{Gabelli1988,
abstract = {If $A$ is a domain with the ascending chain condition on (integral) invertible ideals, then the group $I(A)$ of its invertible ideals is generated by the set $I_\{m\}(A)$ of maximal invertible ideals. In this note we study some properties of $I_\{m\}(A)$ and we prove that, if $I(A)$ is a free group on $I_\{m\}(A)$, then $A$ is a locally factorial Krull domain.},
author = {Gabelli, Stefania},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Krull domain; Locally factorial; Invertible ideal; integral domain; ascending chain condition; invertible ideals; divisorial ideal; locally factorial Krull domain},
language = {eng},
month = {9},
number = {3},
pages = {419-422},
publisher = {Accademia Nazionale dei Lincei},
title = {On domains with ACC on invertible ideals},
url = {http://eudml.org/doc/287370},
volume = {82},
year = {1988},
}
TY - JOUR
AU - Gabelli, Stefania
TI - On domains with ACC on invertible ideals
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1988/9//
PB - Accademia Nazionale dei Lincei
VL - 82
IS - 3
SP - 419
EP - 422
AB - If $A$ is a domain with the ascending chain condition on (integral) invertible ideals, then the group $I(A)$ of its invertible ideals is generated by the set $I_{m}(A)$ of maximal invertible ideals. In this note we study some properties of $I_{m}(A)$ and we prove that, if $I(A)$ is a free group on $I_{m}(A)$, then $A$ is a locally factorial Krull domain.
LA - eng
KW - Krull domain; Locally factorial; Invertible ideal; integral domain; ascending chain condition; invertible ideals; divisorial ideal; locally factorial Krull domain
UR - http://eudml.org/doc/287370
ER -
References
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