Geodesic
RINGS OVER WHICH CYCLICS ARE DIRECT SUMS OF PROJECTIVE AND CS OR NOETHERIAN*
Glasgow mathematical journal, Tome 52 (2010) no. A, pp. 103-110

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

DOI

R is called a right WV-ring if each simple right R-module is injective relative to proper cyclics. If R is a right WV-ring, then R is right uniform or a right V-ring. It is shown that a right WV-ring R is right noetherian if and only if each right cyclic module is a direct sum of a projective module and a CS (complements are summands, a.k.a. ‘extending modules’) or noetherian module. For a finitely generated module M with projective socle over a V-ring R such that every subfactor of M is a direct sum of a projective module and a CS or noetherian module, we show M = X ⊕ T, where X is semisimple and T is noetherian with zero socle. In the case where M = R, we get R = S ⊕ T, where S is a semisimple artinian ring and T is a direct sum of right noetherian simple rings with zero socle. In addition, if R is a von Neumann regular ring, then it is semisimple artinian.
DOI : 10.1017/S0017089510000200
Mots-clés : 16D50, 16D70, 16D80 
HOLSTON, C. J.; JAIN, S. K.; LEROY, A. RINGS OVER WHICH CYCLICS ARE DIRECT SUMS OF PROJECTIVE AND CS OR NOETHERIAN*. Glasgow mathematical journal, Tome 52 (2010) no. A, pp. 103-110. doi: 10.1017/S0017089510000200
@article{10_1017_S0017089510000200,
     author = {HOLSTON, C. J. and JAIN, S. K. and LEROY, A.},
     title = {RINGS {OVER} {WHICH} {CYCLICS} {ARE} {DIRECT} {SUMS} {OF} {PROJECTIVE} {AND} {CS} {OR} {NOETHERIAN*}},
     journal = {Glasgow mathematical journal},
     pages = {103--110},
     year = {2010},
     volume = {52},
     number = {A},
     doi = {10.1017/S0017089510000200},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000200/}
}
TY  - JOUR
AU  - HOLSTON, C. J.
AU  - JAIN, S. K.
AU  - LEROY, A.
TI  - RINGS OVER WHICH CYCLICS ARE DIRECT SUMS OF PROJECTIVE AND CS OR NOETHERIAN*
JO  - Glasgow mathematical journal
PY  - 2010
SP  - 103
EP  - 110
VL  - 52
IS  - A
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000200/
DO  - 10.1017/S0017089510000200
ID  - 10_1017_S0017089510000200
ER  - 
%0 Journal Article
%A HOLSTON, C. J.
%A JAIN, S. K.
%A LEROY, A.
%T RINGS OVER WHICH CYCLICS ARE DIRECT SUMS OF PROJECTIVE AND CS OR NOETHERIAN*
%J Glasgow mathematical journal
%D 2010
%P 103-110
%V 52
%N A
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000200/
%R 10.1017/S0017089510000200
%F 10_1017_S0017089510000200

Cité par Sources :