Annihilator-small submodules

Tayyebeh Amouzegar-Kalati; Derya Keskin-Tütüncü

Annihilator-small submodules

Tayyebeh Amouzegar-Kalati
, Derya Keskin-Tütüncü

Division of Algebra and Number Theory

Quchan University of Technology

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1053-1063
Number of pages	11
Journal	Bulletin of the Iranian Mathematical Society
Volume	39
Issue number	6
Publication status	Published - Dec 2013

Keywords

Annihilator-small submodules
Annihilators
Small submodules

Cite this

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title = "Annihilator-small submodules",

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AU - Amouzegar-Kalati, Tayyebeh

AU - Keskin-Tütüncü, Derya

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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

Abstract

Keywords

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