Rad-Supplemented Modules
Engin Büyükașik
Izmir Institute of Technology, TurkeyEngin Mermut
Dokuz Eylül Üniversiteși, Buca/izmir, TurkeySalahattin Özdemir
Dokuz Eylül Üniversiteși, Buca/izmir, Turkey
Abstract
Let be a radical for the category of left -modules for a ring . If is a -coatomic module, that is, if has no nonzero -torsion factor module, then is small in . If is a -supplement in , then the intersection of and is . In particular, if is a -supplement in , then the intersection of and is . A module is -supplemented if and only if the factor module of by is -supplemented where is the sum of all -torsion submodules of . Every left -module is -supplemented if and only if the direct sum of countably many copies of is a -supplemented left -module if and only if every reduced left -module is supplemented if and only if is left perfect where is the sum of all left ideals of such that . For a left duo ring , is a -supplemented left -module if and only if is semiperfect. For a Dedekind domain , an -module is -supplemented if and only if is supplemented where is the divisible part of .
Cite this article
Engin Büyükașik, Engin Mermut, Salahattin Özdemir, Rad-Supplemented Modules. Rend. Sem. Mat. Univ. Padova 124 (2010), pp. 157–177
DOI 10.4171/RSMUP/124-10