The construction of mixed modules from torsion modules

1994 ◽  
Vol 62 (3) ◽  
pp. 199-202 ◽  
Author(s):  
R�diger G�bel ◽  
Warren May
Keyword(s):  
Torsion Modules

scholarly journals Torsion and protorsion modules over free ideal rings

1970 ◽  
Vol 11 (4) ◽  
pp. 490-498
Author(s):  
P. M. Cohn
Keyword(s):  
Principal Ideal ◽  
Finitely Generated ◽  
Commutative Case ◽  
Principal Ideal Domains ◽  
Torsion Modules ◽  
Noncommutative Analogue

Free ideal rings (or firs, cf. [2, 3] and § 2 below) form a noncommutative analogue of principal ideal domains, to which they reduce in the commutative case, and in [3] a category TR of right R-modules was defined, over any fir R, which forms an analogue of finitely generated torsion modules. The category TR was shown to be abelian, and all its objects have finite composition length; more over, the corresponding category RT of left R-modules is dual to TR.

scholarly journals Boundedness of direct products of torsion modules

1986 ◽  
Vol 39 ◽  
pp. 251-273 ◽  
Author(s):  
K.R. Goodearl ◽  
B. Zimmermann-Huisgen
Keyword(s):  
Direct Products ◽  
Torsion Modules

A GENERALIZATION OF BAER'S LOWER NILRADICAL FOR MODULES

2007 ◽  
Vol 06 (02) ◽  
pp. 337-353 ◽  
Author(s):  
MAHMOOD BEHBOODI
Keyword(s):  
Prime Ring ◽  
Artinian Ring ◽  
Prime Radical ◽  
Nilpotent Elements ◽  
Noetherian Domain ◽  
Prime Submodules ◽  
Strongly Nilpotent ◽  
Commutative Domain ◽  
Torsion Modules

Let M be a left R-module. A proper submodule P of M is called classical prime if for all ideals [Formula: see text] and for all submodules N ⊆ M, [Formula: see text] implies that [Formula: see text] or [Formula: see text]. We generalize the Baer–McCoy radical (or classical prime radical) for a module [denoted by cl.rad R(M)] and Baer's lower nilradical for a module [denoted by Nil *(RM)]. For a module RM, cl.rad R(M) is defined to be the intersection of all classical prime submodules of M and Nil *(RM) is defined to be the set of all strongly nilpotent elements of M (defined later). It is shown that, for any projective R-module M, cl.rad R(M) = Nil *(RM) and, for any module M over a left Artinian ring R, cl.rad R(M) = Nil *(RM) = Rad (M) = Jac (R)M. In particular, if R is a commutative Noetherian domain with dim (R) ≤ 1, then for any module M, we have cl.rad R(M) = Nil *(RM). We show that over a left bounded prime left Goldie ring, the study of Baer–McCoy radicals of general modules reduces to that of torsion modules. Moreover, over an FBN prime ring R with dim (R) ≤ 1 (or over a commutative domain R with dim (R) ≤ 1), every semiprime submodule of any module is an intersection of classical prime submodules.

Torsion modules

2000 ◽  
pp. 463-488
Author(s):  
László Fuchs ◽  
Luigi Salce
Keyword(s):  
Torsion Modules

Torsion modules and ideal transforms

2012 ◽  
pp. 16-46
Author(s):  
M. P. Brodmann ◽  
R. Y. Sharp
Keyword(s):  
Torsion Modules

On P-torsion modules over a pullback of two Dedekind domains

2012 ◽  
Vol 19 (3) ◽  
Author(s):  
Shahabaddin Ebrahimi Atani ◽  
Fatemeh Esmaeili Khalil Saraei
Keyword(s):  
Dedekind Domains ◽  
Torsion Modules
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