Geodesic
GOLDIE*-SUPPLEMENTED MODULES
Glasgow mathematical journal, Tome 52 (2010) no. A, pp. 41-52

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

Motivated by a relation on submodules of a module used by both A. W. Goldie and P. F. Smith, we say submodules X, Y of M are β* equivalent, Xβ*Y, if and only if is small in and is small in . We show that the β* relation is an equivalence relation and has good behaviour with respect to addition of submodules, homomorphisms and supplements. We apply these results to introduce the class of -supplemented modules and to investigate this class and the class of H-supplemented modules. These classes are located among various well-known classes of modules related to the class of lifting modules. Moreover these classes are used to explore an open question of S. H. Mohamed and B. J. Mueller. Examples are provided to illustrate and delimit the theory.
DOI : 10.1017/S0017089510000212
Mots-clés : 16D10, 16D50 
BIRKENMEIER, G. F.; MUTLU, F. TAKIL; NEBİYEV, C.; SOKMEZ, N.; TERCAN, A. GOLDIE*-SUPPLEMENTED MODULES. Glasgow mathematical journal, Tome 52 (2010) no. A, pp. 41-52. doi: 10.1017/S0017089510000212
@article{10_1017_S0017089510000212,
     author = {BIRKENMEIER, G. F. and MUTLU, F. TAKIL and NEB\.IYEV, C. and SOKMEZ, N. and TERCAN, A.},
     title = {GOLDIE*-SUPPLEMENTED {MODULES}},
     journal = {Glasgow mathematical journal},
     pages = {41--52},
     year = {2010},
     volume = {52},
     number = {A},
     doi = {10.1017/S0017089510000212},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000212/}
}
TY  - JOUR
AU  - BIRKENMEIER, G. F.
AU  - MUTLU, F. TAKIL
AU  - NEBİYEV, C.
AU  - SOKMEZ, N.
AU  - TERCAN, A.
TI  - GOLDIE*-SUPPLEMENTED MODULES
JO  - Glasgow mathematical journal
PY  - 2010
SP  - 41
EP  - 52
VL  - 52
IS  - A
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000212/
DO  - 10.1017/S0017089510000212
ID  - 10_1017_S0017089510000212
ER  - 
%0 Journal Article
%A BIRKENMEIER, G. F.
%A MUTLU, F. TAKIL
%A NEBİYEV, C.
%A SOKMEZ, N.
%A TERCAN, A.
%T GOLDIE*-SUPPLEMENTED MODULES
%J Glasgow mathematical journal
%D 2010
%P 41-52
%V 52
%N A
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000212/
%R 10.1017/S0017089510000212
%F 10_1017_S0017089510000212

[1] 1.Akalan, E., Birkenmeier, G. F. and Tercan, A., Goldie Extending Modules, Commun. Algebra 37 (2), (2009), 663–683. Google Scholar | DOI

[2] 2.Clark, J., Lomp, C., Vanaja, N. and Wisbauer, , Lifting modules: supplements and projectivity in module theory (Birkhäuser Verlag, Basel, Switzerland, 2006). Google Scholar

[3] 3.Fuchs, L., Infinite Abelian Groups (Academic Press, New York, 1970). Google Scholar

[4] 4.Goldie, A. W., Semi-prime rings with maximum condition, Proc. Lond. Math. Soc., 10 (1960), 201–220. Google Scholar | DOI

[5] 5.Kosan, T. and Keskin, D., H-supplemented duo modules, J. Algebra Appl. 6, (2007), 965–971. Google Scholar | DOI

[6] 6.Mohamed, S. H. and Muller, B. J., Continuous and discrete modules, London Mathematical Society Lecture Note Series, (Cambridge University Press, Cambridge, 1990). Google Scholar | DOI

[7] 7.Smith, P. F., Modules for which every submodule has a unique closure, in Ring theory Proceedings of the biennial Ohio state - Denison conference 1992 (Jain, S. K. and Rizvi, S. T., Editors) (World Scientific, Singapore, 1993), 302–313. Google Scholar

[8] 8.Wisbauer, R., Foundations of module and ring theory (Gordon and Breach, Philadelphia, 1991). Google Scholar

Cité par Sources :