ON FULLY IDEMPOTENT MODULES
Küçük Resim Yok
Tarih
2011
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Taylor & Francis Inc
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
A submodule N of a module M is idempotent if N = Hom (M,N)N. The module M is fully idempotent if every submodule of M is idempotent. We prove that over a commutative ring, cyclic idempotent submodules of any module are direct summands. Counterexamples are given to show that this result is not true in general. It is shown that over commutative Noetherian rings, the fully idempotent modules are precisely the semisimple modules. We also show that the commutative rings over which every module is fully idempotent are exactly the semisimple rings. Idempotent submodules of free modules are characterized.
Açıklama
Anahtar Kelimeler
Fully idempotent module, Idempotent submodule
Kaynak
Communications in Algebra
WoS Q Değeri
Q4
Scopus Q Değeri
Q2
Cilt
39
Sayı
8
