M-CANONICAL IDEALS IN INTEGRAL-DOMAINS

Authors
HEINZER WJ HUCKABA JA PAPICK IJ
Citation
Wj. Heinzer et al., M-CANONICAL IDEALS IN INTEGRAL-DOMAINS, Communications in algebra, 26(9), 1998, pp. 3021-3043
Citations number
19
Categorie Soggetti
Mathematics,Mathematics
Journal title
Communications in algebra → ACNP
ISSN journal
00927872
Volume
26
Issue
9
Year of publication
1998
Pages
3021 - 3043
Database
ISI
SICI code
0092-7872(1998)26:9<3021:MIII>2.0.ZU;2-S
Abstract
We prove that a Prufer domain R has an m-canonical ideal I, that is, a n ideal I such that I : (I : J) = J for every ideal J of R, if and onl y if R is h-local with only finitely many maximal ideals that are not finitely generated; moreover, if these conditions are satisfied, then the product of the non-finitely generated maximal ideals is an m-canon ical ideal of R.