Akademik Veri Yönetim Sistemi
RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA, cilt.124, ss.157-177, 2010 (SCI-Expanded)
Let tau be a radical for the category of left R-modules for a ring R. If M is a tau-coatomic module, that is, if M has no nonzero tau-torsion factor module, then tau(M) is small in M. If V is a tau-supplement in M, then the intersection of V and tau(M) is tau(V). In particular, if V is a Rad-supplement in M, then the intersection of V and Rad(M) is Rad(V). A module M is tau-supplemented if and only if the factor module of M by P-tau(M) is v-supplemented where P-tau(M) is the sum of all tau-torsion submodules of M. Every left R-module is Rad-supplemented if and only if the direct sum of countably many copies of R is a Radsupplemented left R-module if and only if every reduced left R-module is supplemented if and only if RIP(R) is left perfect where P(R) is the sum of all left ideals I of R such that RadI = I. For a left duo ring R, R is a Rad-supplemented left R-module if and only if R/P(R) is semiperfect. For a Dedekind domain R, an R-module M is Bad-supplemented if and only if M/D is supplemented where D is the divisible part of M.