Integrally Closed Condensed Domains are Bézout
Canadian mathematical bulletin, Tome 28 (1985) no. 1, pp. 98-102
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It is proved that an integral domain R is a Bézout domain if (and only if) R is integrally closed and I J = {ij|i ∊ I, j ∊ J} for all ideals I and J of R; that is, if (and only if) R is an integrally closed condensed domain. The article then introduces a weakening of the "condensed" concept which, in the context of the k + M construction, is equivalent to a certain field-theoretic condition. Finally, the field extensions satisfying this condition are classified.
Anderson, David F.; Arnold, Jimmy T.; Dobbs, David E. Integrally Closed Condensed Domains are Bézout. Canadian mathematical bulletin, Tome 28 (1985) no. 1, pp. 98-102. doi: 10.4153/CMB-1985-010-x
@article{10_4153_CMB_1985_010_x,
author = {Anderson, David F. and Arnold, Jimmy T. and Dobbs, David E.},
title = {Integrally {Closed} {Condensed} {Domains} are {B\'ezout}},
journal = {Canadian mathematical bulletin},
pages = {98--102},
year = {1985},
volume = {28},
number = {1},
doi = {10.4153/CMB-1985-010-x},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1985-010-x/}
}
TY - JOUR AU - Anderson, David F. AU - Arnold, Jimmy T. AU - Dobbs, David E. TI - Integrally Closed Condensed Domains are Bézout JO - Canadian mathematical bulletin PY - 1985 SP - 98 EP - 102 VL - 28 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1985-010-x/ DO - 10.4153/CMB-1985-010-x ID - 10_4153_CMB_1985_010_x ER -
%0 Journal Article %A Anderson, David F. %A Arnold, Jimmy T. %A Dobbs, David E. %T Integrally Closed Condensed Domains are Bézout %J Canadian mathematical bulletin %D 1985 %P 98-102 %V 28 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1985-010-x/ %R 10.4153/CMB-1985-010-x %F 10_4153_CMB_1985_010_x
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