Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/2523
Title: Rad-supplemented modules
Authors: Büyükaşık, Engin
Mermut, Engin
Özdemir, Salahattin
Keywords: Relative homological algebra
R-modules
General module theory
Local rings
Issue Date: 2010
Publisher: Universita di Padova
Source: Büyükaşık, E., Mermut, E., and Özdemir, S. (2010). Rad-supplemented modules. Mathematical Journal of the University of Padova, 124, 157-177. doi:10.4171/RSMUP/124-10
Abstract: Let τ be a radical for the category of left R-modules for a ring R. If M is a τ-coatomic module, that is, if M has no nonzero τ-torsion factor module, then τ(M) is small in M. If V is a τ-supplement in M, then the intersection of V and τ(M) is τ(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 τ-supplemented if and only if the factor module of M by P τ(M) is τ-supplemented where P τ(M) is the sum of all τ-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 Rad-supplemented left R-module if and only if every reduced left R-module is supplemented if and only if R/P(R) is left perfect where P(R) is the sum of all left ideals I of R such that Rad I = 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 Rad-supplemented if and only if M/D is supplemented where D is the divisible part of M.
URI: http://doi.org/10.4171/RSMUP/124-10
http://hdl.handle.net/11147/2523
ISSN: 0041-8994
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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