Simple divisible modules

1973 ◽  
pp. 79-84
Author(s):  
Eben Matlis
Keyword(s):  
Divisible Modules

scholarly journals Weakly divisible and divisible modules

1982 ◽  
Vol 6 (2) ◽  
pp. 195-200 ◽  
Author(s):  
Shoji Morimoto
Keyword(s):  
Divisible Modules

Q-Divisible Modules

1971 ◽  
Vol 14 (4) ◽  
pp. 491-494 ◽  
Author(s):  
Efraim P. Armendariz
Keyword(s):  
Quotient Ring ◽  
Torsion Class ◽  
Direct Sums ◽  
Factor Module ◽  
Left Quotient ◽  
Divisible Modules

Let R be a ring with 1 and let Q denote the maximal left quotient ring of R [6]. In a recent paper [12], Wei called a (left). R-module M divisible in case HomR (Q, N)≠0 for each nonzero factor module N of M. Modifying the terminology slightly we call such an R-module a Q-divisible R-module. As shown in [12], the class D of all Q-divisible modules is closed under factor modules, extensions, and direct sums and thus is a torsion class in the sense of Dickson [5].

Bicommutators Of Cofaithful, Fully Divisible Modules*: Corrigendum

1974 ◽  
Vol 26 (1) ◽  
pp. 256-256 ◽  
Author(s):  
John A. Beachy
Keyword(s):  
Divisible Modules

S-divisible modules over domains

1992 ◽  
Vol 4 (4) ◽  
Author(s):  
Laszlo Fuchs ◽  
Luigi Salce
Keyword(s):  
Divisible Modules

scholarly journals On divisible modules over valuation domains

1987 ◽  
Vol 110 (2) ◽  
pp. 498-506 ◽  
Author(s):  
L Fuchs
Keyword(s):  
Valuation Domains ◽  
Divisible Modules

Torsion-Free and Divisible Modules Over Finite-Dimensional Algebras

1996 ◽  
Vol 39 (1) ◽  
pp. 111-114
Author(s):  
F. Okoh
Keyword(s):  
Rational Functions ◽  
Indecomposable Module ◽  
Torsion Theory ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Dynkin Diagrams ◽  
The Status ◽  
Hereditary Algebras ◽  
Divisible Modules ◽  
Torsion Free

AbstractIf R is a Dedekind domain, then div splits i.e.; the maximal divisible submodule of every R-module M is a direct summand of M. We investigate the status of this result for some finite-dimensional hereditary algebras. We use a torsion theory which permits the existence of torsion-free divisible modules for such algebras. Using this torsion theory we prove that the algebras obtained from extended Coxeter- Dynkin diagrams are the only such hereditary algebras for which div splits. The field of rational functions plays an essential role. The paper concludes with a new type of infinite-dimensional indecomposable module over a finite-dimensional wild hereditary algebra.

Divisible modules codivisible modules and quasi-divisible modules

1977 ◽  
Vol 5 (6) ◽  
pp. 591-610 ◽  
Author(s):  
K. Nishida
Keyword(s):  
Divisible Modules

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
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