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

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DOI

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/}
}
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AU  - MUTLU, F. TAKIL
AU  - NEBİYEV, C.
AU  - SOKMEZ, N.
AU  - TERCAN, A.
TI  - GOLDIE*-SUPPLEMENTED MODULES
JO  - Glasgow mathematical journal
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%A MUTLU, F. TAKIL
%A NEBİYEV, C.
%A SOKMEZ, N.
%A TERCAN, A.
%T GOLDIE*-SUPPLEMENTED MODULES
%J Glasgow mathematical journal
%D 2010
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%N A
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%R 10.1017/S0017089510000212
%F 10_1017_S0017089510000212

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