scholarly journals Divisible modules over integral domains

1988 ◽  
Vol 26 (1-2) ◽  
pp. 67-85 ◽  
Author(s):  
A. Facchini
Keyword(s):  
Integral Domains ◽  
Divisible Modules

Torsion-Free and Divisible Modules Over Non-Integral-Domains

1963 ◽  
Vol 15 ◽  
pp. 132-151 ◽  
Author(s):  
Lawrence Levy
Keyword(s):  
Commutative Case ◽  
Integral Domains ◽  
Divisible Modules ◽  
Free Modules ◽  
Torsion Free

In trying to extend the concept of torsion to rings more general than commutative integral domains the first thing that we notice is that if the definition is carried over word for word, integral domains are the only rings with torsion-free modules. Thus, if m is an element of any right module M over a ring containing a pair of non-zero elements x and y such that xy = 0, then either mx = 0 or (mx)y = 0. A second difficulty arises in the non-commutative case: Does the set of torsion elements of M form a submodule? The answer to this question will not even be "yes" for arbitrary non-commutative integral domains.

Simple Divisible Modules Over Integral Domains

1989 ◽  
Vol 32 (2) ◽  
pp. 230-240
Author(s):  
Alberto Facchini
Keyword(s):  
Endomorphism Rings ◽  
Integral Domains ◽  
Divisible Module ◽  
Divisible Modules

AbstractAn R-module is a simple divisible module if it is a nonzero divisible module that has no proper non-zero divisible submodules. We study simple divisible modules and their endomorphism rings, give some examples and determine all simple divisible modules over some classes of rings.

scholarly journals h-Divisible modules over integral domains

2011 ◽  
Vol 330 (1) ◽  
pp. 76-85 ◽  
Author(s):  
Sang Bum Lee
Keyword(s):  
Integral Domains ◽  
Divisible Modules

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 Integrally closed factor domains

1988 ◽  
Vol 37 (3) ◽  
pp. 353-366 ◽  
Author(s):  
Valentina Barucci ◽  
David E. Dobbs ◽  
S.B. Mulay
Keyword(s):  
Prime Ideal ◽  
The Other ◽  
Integral Domains ◽  
Other Hand ◽  
Dedekind Domains ◽  
Integrally Closed

This paper characterises the integral domains R with the property that R/P is integrally closed for each prime ideal P of R. It is shown that Dedekind domains are the only Noetherian domains with this property. On the other hand, each integrally closed going-down domain has this property. Related properties and examples are also studied.

Graded integral domains in which each nonzero homogeneous t-ideal is divisorial

2019 ◽  
Vol 18 (01) ◽  
pp. 1950018 ◽  
Author(s):  
Gyu Whan Chang ◽  
Haleh Hamdi ◽  
Parviz Sahandi
Keyword(s):  
Integral Domain ◽  
Nonzero Ideal ◽  
Integral Domains ◽  
Cancellative Monoid ◽  
Integrally Closed ◽  
Graded Integral Domain

Let [Formula: see text] be a nonzero commutative cancellative monoid (written additively), [Formula: see text] be a [Formula: see text]-graded integral domain with [Formula: see text] for all [Formula: see text], and [Formula: see text]. In this paper, we study graded integral domains in which each nonzero homogeneous [Formula: see text]-ideal (respectively, homogeneous [Formula: see text]-ideal) is divisorial. Among other things, we show that if [Formula: see text] is integrally closed, then [Formula: see text] is a P[Formula: see text]MD in which each nonzero homogeneous [Formula: see text]-ideal is divisorial if and only if each nonzero ideal of [Formula: see text] is divisorial, if and only if each nonzero homogeneous [Formula: see text]-ideal of [Formula: see text] is divisorial.

scholarly journals On integral domains whose overrings are Kaplansky ideal transforms

2001 ◽  
Vol 163 (2) ◽  
pp. 173-192 ◽  
Author(s):  
Marco Fontana ◽  
Evan Houston
Keyword(s):  
Integral Domains
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