Geodesic
On Extensions of Weakly Primitive Rings
Canadian journal of mathematics, Tome 32 (1980) no. 4, pp. 937-944

Voir la notice de l'article provenant de la source Cambridge University Press

If R is a ring an R-module M is called compressible when it can be embedded in each of its non-zero submodules; and M is called monoform if each partial endomorphism N → M, N ⊆ M, is either zero or monic. The ring R is called (left) weakly primitive if it has a faithful monoform compressible left module. It is known that a version of the Jacobson density theorem holds for weakly primitive rings [4], and that weak primitivity is a Mori ta invariant and is inherited by a variety of subrings and matrix rings. The purpose of this paper is to show that weak primitivity is preserved under formation of polynomials, rings of quotients, and group rings of torsion-free abelian groups. The key result is that R[x] is weakly primitive when R is (Theorem 1). 
Nicholson, W. K.; Waiters, J. F.; Zelmanowitz, J. M. On Extensions of Weakly Primitive Rings. Canadian journal of mathematics, Tome 32 (1980) no. 4, pp. 937-944. doi: 10.4153/CJM-1980-071-6
@article{10_4153_CJM_1980_071_6,
     author = {Nicholson, W. K. and Waiters, J. F. and Zelmanowitz, J. M.},
     title = {On {Extensions} of {Weakly} {Primitive} {Rings}},
     journal = {Canadian journal of mathematics},
     pages = {937--944},
     year = {1980},
     volume = {32},
     number = {4},
     doi = {10.4153/CJM-1980-071-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1980-071-6/}
}
TY  - JOUR
AU  - Nicholson, W. K.
AU  - Waiters, J. F.
AU  - Zelmanowitz, J. M.
TI  - On Extensions of Weakly Primitive Rings
JO  - Canadian journal of mathematics
PY  - 1980
SP  - 937
EP  - 944
VL  - 32
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1980-071-6/
DO  - 10.4153/CJM-1980-071-6
ID  - 10_4153_CJM_1980_071_6
ER  - 
%0 Journal Article
%A Nicholson, W. K.
%A Waiters, J. F.
%A Zelmanowitz, J. M.
%T On Extensions of Weakly Primitive Rings
%J Canadian journal of mathematics
%D 1980
%P 937-944
%V 32
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1980-071-6/
%R 10.4153/CJM-1980-071-6
%F 10_4153_CJM_1980_071_6

[1] 1. Connell, I. G., On the group ring, Can. J. Math. 15 (1963), 650–685. Google Scholar

[2] 2. Lawrence, J., The coefficient ring of a primitive group ring, Can. J. Math. 27 (1975), 489–494. Google Scholar

[3] 3. Stenström, B., Rings of quotients (Springer-Verlag, New York, 1975). Google Scholar | DOI

[4] 4. Zelmanowitz, J., Dense rings of linear transformations, Ring Theory II, Proceedings of the Second Oklahoma Conference (Marcel Dekker, New York, 1977). Google Scholar

Cité par Sources :