Modules with Finitely Many Submodules

S. Akbari; S. Khalashi Ghezelahmad; E. Yaraneri

doi:10.1142/S1005386716000444

Modules with Finitely Many Submodules

S. Akbari
, S. Khalashi Ghezelahmad
, E. Yaraneri

Matematik Bölümü

Sharif University of Technology
Institute for Research for Fundamental Sciences
Iran University of Science and Technology

Araştırma sonucu: Dergiye katkı › Makale › bilirkişi

1 Atıf (Scopus)

Özet

In this paper, we study modules having only finitely many submodules over any ring which is not necessarily commutative. We try to understand how such a module decomposes as a direct sum. We justify that any module V having only finitely many submodules over any ring A is an extension of a cyclic A-module by a finite A-module. Under some assumptions on A, such as commutativity of A, we prove that an A-module V has finitely many submodules if and only if V can be written as a direct sum of a cyclic A-module having only finitely many A-submodules and a finite A-module.

Orijinal dil	İngilizce
Sayfa (başlangıç-bitiş)	463-468
Sayfa sayısı	6
Dergi	Algebra Colloquium
Hacim	23
Basın numarası	3
DOI'lar	https://doi.org/10.1142/S1005386716000444
Yayın durumu	Yayınlandı - 1 Eyl 2016

Bibliyografik not

Publisher Copyright:
© 2016 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and Suzhou University.

Finansman

The first author is indebted to School of Mathematics, Institute for Research in Funda-mental Sciences (IPM) for support. The research of the first author was supported in part by a grant from IPM (No. 93050212).

Finansörler
Institute for Research in Funda-mental Sciences
Institute for Research in Fundamental Sciences

Belgeye Erişim

10.1142/S1005386716000444

Diğer Dosyalar ve Linkler

Link to publication in Scopus

Alıntı Yap

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title = "Modules with Finitely Many Submodules",

abstract = "In this paper, we study modules having only finitely many submodules over any ring which is not necessarily commutative. We try to understand how such a module decomposes as a direct sum. We justify that any module V having only finitely many submodules over any ring A is an extension of a cyclic A-module by a finite A-module. Under some assumptions on A, such as commutativity of A, we prove that an A-module V has finitely many submodules if and only if V can be written as a direct sum of a cyclic A-module having only finitely many A-submodules and a finite A-module.",

keywords = "direct sum, module, submodule",

author = "S. Akbari and Ghezelahmad, \{S. Khalashi\} and E. Yaraneri",

note = "Publisher Copyright: {\textcopyright} 2016 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and Suzhou University.",

year = "2016",

month = sep,

day = "1",

doi = "10.1142/S1005386716000444",

language = "English",

volume = "23",

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journal = "Algebra Colloquium",

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TY - JOUR

T1 - Modules with Finitely Many Submodules

AU - Akbari, S.

AU - Ghezelahmad, S. Khalashi

AU - Yaraneri, E.

PY - 2016/9/1

Y1 - 2016/9/1

N2 - In this paper, we study modules having only finitely many submodules over any ring which is not necessarily commutative. We try to understand how such a module decomposes as a direct sum. We justify that any module V having only finitely many submodules over any ring A is an extension of a cyclic A-module by a finite A-module. Under some assumptions on A, such as commutativity of A, we prove that an A-module V has finitely many submodules if and only if V can be written as a direct sum of a cyclic A-module having only finitely many A-submodules and a finite A-module.

AB - In this paper, we study modules having only finitely many submodules over any ring which is not necessarily commutative. We try to understand how such a module decomposes as a direct sum. We justify that any module V having only finitely many submodules over any ring A is an extension of a cyclic A-module by a finite A-module. Under some assumptions on A, such as commutativity of A, we prove that an A-module V has finitely many submodules if and only if V can be written as a direct sum of a cyclic A-module having only finitely many A-submodules and a finite A-module.

KW - direct sum

KW - module

KW - submodule

UR - https://www.scopus.com/pages/publications/84975461288

U2 - 10.1142/S1005386716000444

DO - 10.1142/S1005386716000444

M3 - Article

AN - SCOPUS:84975461288

SN - 1005-3867

VL - 23

SP - 463

EP - 468

JO - Algebra Colloquium

JF - Algebra Colloquium

IS - 3

ER -

Modules with Finitely Many Submodules

Özet

Bibliyografik not

Finansman

Belgeye Erişim

Diğer Dosyalar ve Linkler

Parmak izi

Alıntı Yap