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 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.

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 Endomorphism Rings Via Minimal Morphisms

2021 ◽  
Vol 18 (4) ◽  
Author(s):  
Manuel Cortés-Izurdiaga ◽  
Pedro A. Guil Asensio ◽  
D. Keskin Tütüncü ◽  
Ashish K. Srivastava
Keyword(s):  
Endomorphism Rings

On the computation of the endomorphism rings of abelian surfaces

2021 ◽  
Author(s):  
Claus Fieker ◽  
Tommy Hofmann ◽  
Sogo Pierre Sanon
Keyword(s):  
Abelian Surfaces ◽  
Endomorphism Rings

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.

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