Prime and Primary Ideals in a Prüfer Order in a Simple Artinian Ring with Finite Dimension over its Center
Canadian mathematical bulletin, Tome 42 (1999) no. 3, pp. 371-379
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Let $Q$ be a simple Artinian ring with finite dimension over its center. An order $R$ in $Q$ is said to be Prüfer if any one-sided $R$ -ideal is a progenerator. We study prime and primary ideals of a Prüfer order under the condition that the center is Prüfer. Also we characterize branched and unbranched prime ideals of a Prüfer order.
Marubayashi, H.; Ueda, A. Prime and Primary Ideals in a Prüfer Order in a Simple Artinian Ring with Finite Dimension over its Center. Canadian mathematical bulletin, Tome 42 (1999) no. 3, pp. 371-379. doi: 10.4153/CMB-1999-043-7
@article{10_4153_CMB_1999_043_7,
author = {Marubayashi, H. and Ueda, A.},
title = {Prime and {Primary} {Ideals} in a {Pr\"ufer} {Order} in a {Simple} {Artinian} {Ring} with {Finite} {Dimension} over its {Center}},
journal = {Canadian mathematical bulletin},
pages = {371--379},
year = {1999},
volume = {42},
number = {3},
doi = {10.4153/CMB-1999-043-7},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1999-043-7/}
}
TY - JOUR AU - Marubayashi, H. AU - Ueda, A. TI - Prime and Primary Ideals in a Prüfer Order in a Simple Artinian Ring with Finite Dimension over its Center JO - Canadian mathematical bulletin PY - 1999 SP - 371 EP - 379 VL - 42 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1999-043-7/ DO - 10.4153/CMB-1999-043-7 ID - 10_4153_CMB_1999_043_7 ER -
%0 Journal Article %A Marubayashi, H. %A Ueda, A. %T Prime and Primary Ideals in a Prüfer Order in a Simple Artinian Ring with Finite Dimension over its Center %J Canadian mathematical bulletin %D 1999 %P 371-379 %V 42 %N 3 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1999-043-7/ %R 10.4153/CMB-1999-043-7 %F 10_4153_CMB_1999_043_7
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