Geodesic
On the Criteria of D.D. Anderson for Invertible and Flat Ideals
Canadian mathematical bulletin, Tome 29 (1986) no. 1, pp. 25-32

Voir la notice de l'article provenant de la source Cambridge

DOI

Let R be an integral domain. It is proved that if a nonzero ideal I of R can be generated by n < ∞ elements, then I is invertible (i.e., flat) if and only if I(∩ Rai) = ∩ Iai for all { a1, . . ., a n} ⊂ I. The article's main focus is on torsion-free R-modules E which are LCM-stable in the sense that E(Ra ∩ Rb) = Ea ∩ Eb for all a, b ∈ R. By means of linear relations, LCM-stableness is shown to be equivalent to a weak aspect of flatness. Consequently, if each finitely generated ideal of R may be 2-generated, then each LCM-stable R-module is flat. Finally, LCM-stableness of maximal ideals serves to characterize Prüfer domains, Dedekind domains, principal ideal domains, and Bézout domains amongst suitably larger classes of integral domains.
DOI : 10.4153/CMB-1986-004-4
Mots-clés : primary 13C11, 13F05, secondary 13G05, 13F15, 13E05, 18G15 
Dobbs, David E. On the Criteria of D.D. Anderson for Invertible and Flat Ideals. Canadian mathematical bulletin, Tome 29 (1986) no. 1, pp. 25-32. doi: 10.4153/CMB-1986-004-4
@article{10_4153_CMB_1986_004_4,
     author = {Dobbs, David E.},
     title = {On the {Criteria} of {D.D.} {Anderson} for {Invertible} and {Flat} {Ideals}},
     journal = {Canadian mathematical bulletin},
     pages = {25--32},
     year = {1986},
     volume = {29},
     number = {1},
     doi = {10.4153/CMB-1986-004-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-004-4/}
}
TY  - JOUR
AU  - Dobbs, David E.
TI  - On the Criteria of D.D. Anderson for Invertible and Flat Ideals
JO  - Canadian mathematical bulletin
PY  - 1986
SP  - 25
EP  - 32
VL  - 29
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-004-4/
DO  - 10.4153/CMB-1986-004-4
ID  - 10_4153_CMB_1986_004_4
ER  - 
%0 Journal Article
%A Dobbs, David E.
%T On the Criteria of D.D. Anderson for Invertible and Flat Ideals
%J Canadian mathematical bulletin
%D 1986
%P 25-32
%V 29
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-004-4/
%R 10.4153/CMB-1986-004-4
%F 10_4153_CMB_1986_004_4

Cité par Sources :