Direct sums of ADS* modules
Küçük Resim Yok
Tarih
2016
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer Basel Ag
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
A module M is called ADS* if for every direct summand N of M and every supplement K of N in M, we have M = N circle plus K. In this work, we study direct sums of ADS* modules. Many examples are provided to show that this notion is not inherited by direct sums. It is shown that if a module M has a decomposition M = A circle plus B which complements direct summands such that A and B are mutually projective, then M is ADS*. The class of rings R, for which all direct sums of ADS* R-modules are ADS*, is shown to be exactly that of the right V-rings. We characterize the class of right perfect rings R for which R circle plus S is ADS* for every simple R-module S as that of the semisimple rings.
Açıklama
Anahtar Kelimeler
Supplement submodule, ADS* module, V-ring
Kaynak
Boletin De La Sociedad Matematica Mexicana
WoS Q Değeri
N/A
Scopus Q Değeri
Q2
Cilt
22
Sayı
1
