A Gorenstein analogue of a result of Bertin

2014 ◽  
Vol 14 (02) ◽  
pp. 1550019 ◽  
Author(s):  
Lei Qiao ◽  
Fanggui Wang
Keyword(s):  
Integral Domain ◽  
Prüfer Domain ◽  
Prufer Domains ◽  
Prüfer Domains ◽  
Gorenstein Flat

An integral domain R is called a Gorenstein Prüfer (G-Prüfer) domain if it is coherent and every submodule of a flat R-module is Gorenstein flat. In this paper, we show that every n-FC domain is an intersection of local G-Prüfer domains. We also give several characterizations of G-Prüfer domains.

scholarly journals Decomposition and classification of length functions

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.

scholarly journals Arithmetic Rings and their generalizations

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.

The Complete Quotient Ring of Images of Semilocal Prüfer Domains

1977 ◽  
Vol 29 (5) ◽  
pp. 914-927 ◽  
Author(s):  
John Chuchel ◽  
Norman Eggert
Keyword(s):  
Homomorphic Image ◽  
Noetherian Ring ◽  
Quotient Ring ◽  
Local Rings ◽  
Topological Ring ◽  
Prüfer Domain ◽  
Prufer Domains ◽  
Prüfer Domains ◽  
Quotient Rings ◽  
Prüfer Rings

It is well known that the complete quotient ring of a Noetherian ring coincides with its classical quotient ring, as shown in Akiba [1]. But in general, the structure of the complete quotient ring of a given ring is largely unknown. This paper investigates the structure of the complete quotient ring of certain Prüfer rings. Boisen and Larsen [2] considered conditions under which a Prüfer ring is a homomorphic image of a Prüfer domain and the properties inherited from the domain. We restrict our investigation primarily to homomorphic images of semilocal Prüfer domains. We characterize the complete quotient ring of a semilocal Prüfer domain in terms of complete quotient rings of local rings and a completion of a topological ring.

FACTORIZATION IN PRÜFER DOMAINS

2017 ◽  
Vol 60 (2) ◽  
pp. 401-409 ◽  
Author(s):  
JIM COYKENDALL ◽  
RICHARD ERWIN HASENAUER
Keyword(s):  
Prüfer Domain ◽  
Prufer Domains ◽  
Prüfer Domains

AbstractWe construct a norm on the nonzero elements of a Prüfer domain and extend this concept to the set of ideals of a Prüfer domain. These norms are used to study factorization properties Prüfer of domains.

scholarly journals Quasi-projectivity over domains

1999 ◽  
Vol 60 (1) ◽  
pp. 129-135
Author(s):  
Dmitri Alexeev
Keyword(s):  
Tensor Product ◽  
Integral Domain ◽  
Quotient Field ◽  
Projective Ideal ◽  
Prufer Domains ◽  
Prüfer Domains

Let R be an integral domain with quotient field Q. We investigate quasi- and Q-projective ideals, and properties of domains all ideals of which are quasi-projective. It is shown that the so-called l½-generated ideals are quasi-projective, moreover, projective. A module M is quasi-projective if and only if, for a projective ideal P of R, the tensor product M ⊗RP is quasi-projective. Domains whose all ideals are quasi-projective are characterised as almost maximal Prüfer domains. Q is quasi-projective if and only if every proper submodule of Q is complete in its R-topology.

scholarly journals MODULES OVER PRÜFER DOMAINS WHICH SATISFY THE RADICAL FORMULA

2007 ◽  
Vol 49 (1) ◽  
pp. 127-131
Author(s):  
DILEK BUYRUK ◽  
DILEK PUSAT-YILMAZ
Keyword(s):  
Prüfer Domain ◽  
Prufer Domains ◽  
Prüfer Domains

Abstract.In this paper we prove that if R is a Prüfer domain, then the R-module R⊕ R satisfies the radical formula.

Divisorial Prime Ideals in Prüfer Domains

1984 ◽  
Vol 27 (3) ◽  
pp. 324-328 ◽  
Author(s):  
Marco Fontana ◽  
James A. Huckaba ◽  
Ira J. Papick
Keyword(s):  
Prime Ideal ◽  
Recent Work ◽  
Prime Ideals ◽  
Prüfer Domain ◽  
Divisorial Ideal ◽  
Prufer Domains ◽  
Prüfer Domains

AbstractGiven a Prüfer domain R and a prime ideal P in R, we study some conditions which force P to be a divisorial ideal of R. This paper extends some recent work of Huckaba and Papick.

scholarly journals π-domains, overrings, and divisorial ideals

1978 ◽  
Vol 19 (2) ◽  
pp. 199-203 ◽  
Author(s):  
D. D. Anderson
Keyword(s):  
Principal Ideal ◽  
Integral Domain ◽  
Prime Ideals ◽  
Unique Factorization ◽  
Unique Factorization Domain ◽  
Prufer Domains ◽  
Interesting Class ◽  
Prüfer Domains ◽  
Krull Domains

In this paper we study several generalizations of the concept of unique factorization domain. An integral domain is called a π-domain if every principal ideal is a product of prime ideals. Theorem 1 shows that the class of π-domains forms a rather natural subclass of the class of Krull domains. In Section 3 we consider overrings of π-domains. In Section 4 generalized GCD-domains are introduced: these form an interesting class of domains containing all Prüfer domains and all π-domains.

On ideal theory in high prufer domains

1975 ◽  
Vol 14 (4) ◽  
pp. 303-336 ◽  
Author(s):  
Moshe Jarden
Keyword(s):  
Ideal Theory ◽  
Prufer Domains ◽  
Prüfer Domains
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