Annihilator-small submodules

Tayyebeh Amouzegar-Kalati; Derya Keskin-Tütüncü

Annihilator-small submodules

Tayyebeh Amouzegar-Kalati
, Derya Keskin-Tütüncü

Cebir ve Sayılar Teorisi Anabilim Dalı

Quchan University of Technology

Araştırma çıktısı: Dergiye katkı › Makale › Hakemli

9 Alıntılar (Scopus)

Özet

Let M_R be a module with S = End(M_R). We call a submodule K of M_R annihilator-small if K + T = M, T a submodule of M_R, implies that ℓ_S(T) = 0, where ℓS indicates the left annihilator of T over S. The sum A_R(M) of all such submodules of M_R contains the Jacobson radical Rad(M) and the left singular submodule Z_S(M). If M_R is cyclic, then A_R(M) is the unique largest annihilator-small submodule of M_R. We study A_R(M) and K_S(M) in this paper. Conditions when A_R(M) is annihilator-small and K_S(M) = J(S) = Tot(M,M) are given.

Orijinal dil	İngilizce
Sayfa (başlangıç-bitiş)	1053-1063
Sayfa sayısı	11
Dergi	Bulletin of the Iranian Mathematical Society
Hacim	39
Basın numarası	6
Yayın durumu	Yayınlandı - Ara 2013

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Link to publication in Scopus

Bundan alıntı yap

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title = "Annihilator-small submodules",

abstract = "Let MR be a module with S = End(MR). We call a submodule K of MR annihilator-small if K + T = M, T a submodule of MR, implies that ℓS(T) = 0, where ℓS indicates the left annihilator of T over S. The sum AR(M) of all such submodules of MR contains the Jacobson radical Rad(M) and the left singular submodule ZS(M). If MR is cyclic, then AR(M) is the unique largest annihilator-small submodule of MR. We study AR(M) and KS(M) in this paper. Conditions when AR(M) is annihilator-small and KS(M) = J(S) = Tot(M,M) are given.",

keywords = "Annihilator-small submodules, Annihilators, Small submodules",

author = "Tayyebeh Amouzegar-Kalati and Derya Keskin-T{\"u}t{\"u}nc{\"u}",

year = "2013",

month = dec,

language = "English",

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journal = "Bulletin of the Iranian Mathematical Society",

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TY - JOUR

T1 - Annihilator-small submodules

AU - Amouzegar-Kalati, Tayyebeh

AU - Keskin-Tütüncü, Derya

PY - 2013/12

Y1 - 2013/12

N2 - Let MR be a module with S = End(MR). We call a submodule K of MR annihilator-small if K + T = M, T a submodule of MR, implies that ℓS(T) = 0, where ℓS indicates the left annihilator of T over S. The sum AR(M) of all such submodules of MR contains the Jacobson radical Rad(M) and the left singular submodule ZS(M). If MR is cyclic, then AR(M) is the unique largest annihilator-small submodule of MR. We study AR(M) and KS(M) in this paper. Conditions when AR(M) is annihilator-small and KS(M) = J(S) = Tot(M,M) are given.

AB - Let MR be a module with S = End(MR). We call a submodule K of MR annihilator-small if K + T = M, T a submodule of MR, implies that ℓS(T) = 0, where ℓS indicates the left annihilator of T over S. The sum AR(M) of all such submodules of MR contains the Jacobson radical Rad(M) and the left singular submodule ZS(M). If MR is cyclic, then AR(M) is the unique largest annihilator-small submodule of MR. We study AR(M) and KS(M) in this paper. Conditions when AR(M) is annihilator-small and KS(M) = J(S) = Tot(M,M) are given.

KW - Annihilator-small submodules

KW - Annihilators

KW - Small submodules

UR - https://www.scopus.com/pages/publications/84889768735

M3 - Article

AN - SCOPUS:84889768735

SN - 1018-6301

VL - 39

SP - 1053

EP - 1063

JO - Bulletin of the Iranian Mathematical Society

JF - Bulletin of the Iranian Mathematical Society

IS - 6

ER -

Annihilator-small submodules

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