ON μ-ESSENTIAL AND μ-<i>M</i>-SINGULAR MODULES

A. Cigdem Ozcan

doi:10.1142/9789812818331_0023

ON μ-ESSENTIAL AND μ-<i>M</i>-SINGULAR MODULES

A. Cigdem Ozcan

Division of Algebra and Number Theory

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

As a generalization of essential submodules Zhou defines a mu-essential submodule provided it has a non-zero intersection with any non-zero submodule in it for any class p. Let M be a module. In this article we study delta-essential submodules as a dual of delta-small submodules of Zhou where delta = {N is an element of sigma[M] : Rej(N, M) = 0} and M = {N is an element of sigma[M] : N << (N) over cap}, and also define mu-M-singular modules as modules N is an element of sigma[M] such that N congruent to K/L for some K is an element of sigma[M] and L is p-essential in K. By M-M-singular modules and S-M-singular modules a characterization of GCO-modules, and by FC-M-singular modules where FC is the class of finitely cogenerated modules, a characterization of semisimple Artinian rings are given.

Original language	English
Title of host publication	Ring Theory 2007, Proceedings
Editors	H Marubayashi, K Masaike, K Oshiro, M Sato
Publisher	World Scientific
Pages	272-283
Number of pages	12
ISBN (Print)	978-981-281-832-4
DOIs	https://doi.org/10.1142/9789812818331_0023
Publication status	Published - 2009
Event	5th China-Japan-Korea International Symposium on Ring Therory 2007 - Tokyo, Japan Duration: 10 Sept 2007 → 15 Sept 2007

Conference

Conference	5th China-Japan-Korea International Symposium on Ring Therory 2007
Country/Territory	Japan
City	Tokyo
Period	10/09/07 → 15/09/07

Keywords

Essential submodule
Singular module

Access to Document

10.1142/9789812818331_0023

Cite this

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title = "ON μ-ESSENTIAL AND μ-M-SINGULAR MODULES",

abstract = "As a generalization of essential submodules Zhou defines a mu-essential submodule provided it has a non-zero intersection with any non-zero submodule in it for any class p. Let M be a module. In this article we study delta-essential submodules as a dual of delta-small submodules of Zhou where delta = \{N is an element of sigma[M] : Rej(N, M) = 0\} and M = \{N is an element of sigma[M] : N << (N) over cap\}, and also define mu-M-singular modules as modules N is an element of sigma[M] such that N congruent to K/L for some K is an element of sigma[M] and L is p-essential in K. By M-M-singular modules and S-M-singular modules a characterization of GCO-modules, and by FC-M-singular modules where FC is the class of finitely cogenerated modules, a characterization of semisimple Artinian rings are given.",

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note = "5th China-Japan-Korea International Symposium on Ring Therory 2007 ; Conference date: 10-09-2007 Through 15-09-2007",

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AU - Ozcan, A. Cigdem

PY - 2009

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N2 - As a generalization of essential submodules Zhou defines a mu-essential submodule provided it has a non-zero intersection with any non-zero submodule in it for any class p. Let M be a module. In this article we study delta-essential submodules as a dual of delta-small submodules of Zhou where delta = {N is an element of sigma[M] : Rej(N, M) = 0} and M = {N is an element of sigma[M] : N << (N) over cap}, and also define mu-M-singular modules as modules N is an element of sigma[M] such that N congruent to K/L for some K is an element of sigma[M] and L is p-essential in K. By M-M-singular modules and S-M-singular modules a characterization of GCO-modules, and by FC-M-singular modules where FC is the class of finitely cogenerated modules, a characterization of semisimple Artinian rings are given.

AB - As a generalization of essential submodules Zhou defines a mu-essential submodule provided it has a non-zero intersection with any non-zero submodule in it for any class p. Let M be a module. In this article we study delta-essential submodules as a dual of delta-small submodules of Zhou where delta = {N is an element of sigma[M] : Rej(N, M) = 0} and M = {N is an element of sigma[M] : N << (N) over cap}, and also define mu-M-singular modules as modules N is an element of sigma[M] such that N congruent to K/L for some K is an element of sigma[M] and L is p-essential in K. By M-M-singular modules and S-M-singular modules a characterization of GCO-modules, and by FC-M-singular modules where FC is the class of finitely cogenerated modules, a characterization of semisimple Artinian rings are given.

KW - Essential submodule

KW - Singular module

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U2 - 10.1142/9789812818331_0023

DO - 10.1142/9789812818331_0023

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BT - Ring Theory 2007, Proceedings

A2 - Marubayashi, H

A2 - Masaike, K

A2 - Oshiro, K

A2 - Sato, M

PB - World Scientific

T2 - 5th China-Japan-Korea International Symposium on Ring Therory 2007

Y2 - 10 September 2007 through 15 September 2007

ER -

ON μ-ESSENTIAL AND μ-<i>M</i>-SINGULAR MODULES

Abstract

Conference

Keywords

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