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

On inert modules over valuation domains

2019 ◽  
Vol 79 (1) ◽  
pp. 120-133
Author(s):  
Luigi Salce
Keyword(s):  
Valuation Domains

scholarly journals An Independence Result on Cotorsion Theories over Valuation Domains

2001 ◽  
Vol 243 (1) ◽  
pp. 294-320 ◽  
Author(s):  
S Bazzoni ◽  
L Salce
Keyword(s):  
Independence Result ◽  
Valuation Domains

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].

scholarly journals On complete integral closure and Archimedean valuation domains

1996 ◽  
Vol 61 (3) ◽  
pp. 377-380 ◽  
Author(s):  
Robert Gilmer
Keyword(s):  
Integral Domain ◽  
Integral Closure ◽  
Extension Field ◽  
Quotient Field ◽  
Valuation Domains ◽  
Complete Integral Closure

AbstractSuppose D is an integral domain with quotient field K and that L is an extension field of K. We show in Theorem 4 that if the complete integral closure of D is an intersection of Archimedean valuation domains on K, then the complete integral closure of D in L is an intersection of Archimedean valuation domains on L; this answers a question raised by Gilmer and Heinzer in 1965.

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