Indecomposed Semilocal Prüfer Domains

Decomposition and classification of length functions

Forum Mathematicum ◽

10.1515/forum-2018-0168 ◽

2020 ◽

Vol 32 (5) ◽

pp. 1109-1129

Author(s):

Dario Spirito

Keyword(s):

Integral Domain ◽

Integral Domains ◽

Bijective Correspondence ◽

Length Functions ◽

Standard Representation ◽

Prufer Domains ◽

Prüfer Domains

AbstractWe study decompositions of length functions on integral domains as sums of length functions constructed from overrings. We find a standard representation when the integral domain admits a Jaffard family, when it is Noetherian and when it is a Prüfer domains such that every ideal has only finitely many minimal primes. We also show that there is a natural bijective correspondence between singular length functions and localizing systems.

Download Full-text

Prüfer domains and pure submodules of direct sums of ideals

Mathematika ◽

10.1112/s0025579300007889 ◽

1999 ◽

Vol 46 (2) ◽

pp. 425-432 ◽

Cited By ~ 2

Author(s):

Bruce Olberding

Keyword(s):

Direct Sums ◽

Prufer Domains ◽

Pure Submodules ◽

Prüfer Domains

Download Full-text

On ideal theory in high prufer domains

manuscripta mathematica ◽

10.1007/bf01169264 ◽

1975 ◽

Vol 14 (4) ◽

pp. 303-336 ◽

Cited By ~ 2

Author(s):

Moshe Jarden

Keyword(s):

Ideal Theory ◽

Prufer Domains ◽

Prüfer Domains

Download Full-text

Arithmetic Rings and their generalizations

Bullettin of the Gioenia Academy of Natural Sciences of Catania ◽

10.35352/gioenia.v51i381.1 ◽

2018 ◽

Vol 51 (381) ◽

pp. FP1-FP6

Author(s):

R. Strano

Keyword(s):

Commutative Ring ◽

Natural Generalization ◽

Prüfer Domain ◽

Prufer Domains ◽

Prüfer Domains

Prüfer domains are characterized by various properties regarding ideals and operations between them. In this note we consider six of these properties. The natural generalization of the notion of Prüfer domain to the case of a commutative ring with unit, not necessarily a domain, is the notion of arithmetic ring. We ask if the previous properties characterize arithmetic ring in the case of a general commutative ring with unit. We prove that four of such properties characterize arithmetic rings while the remaining two are weaker and give rise to two different generalizations.

Download Full-text