TY  - JOUR
TI  - Small supplements, weak supplements and proper classes
AB  - Let SS denote the class of short exact sequences E :0 -> A-> B ->C -> 0 of R-modules and R-module homomorphisms such that f (A)has a small supplement in B i.e. there exists a submodule K of M suchthat f (A) + K = B and f (A) ? K is a small module. It is shown that,SS is a proper class over left hereditary rings. Moreover, in this case,the proper classSS coincides with the smallest proper class containing the class of short exact sequences determined by weak supplementsubmodules. The homological objects, such as,SS-projective and SScoinjective modules are investigated. In order to describe the classSS,we investigate small supplemented modules, i.e. the modules each ofwhose submodule has a small supplement. Besides proving some closure properties of small supplemented modules, we also give a completecharacterization of these modules over Dedekind domains
AU  - DUR?GUN, Yılmaz
AU  - BÜYÜKAŞIK, Engin
AU  - ALİZADE, Rafail
PY  - 2016
JO  - Hacettepe Journal of Mathematics and Statistics
VL  - 45
IS  - 3
SN  - 1303-5010
SP  - 649
EP  - 661
DB  - TRDizin
UR  - http://search/yayin/detay/209056
ER  -