Semisimple (simple) module and length property

Majid Mohammed Abed, Abd. Ghafur Ahmad

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The notion of length module was introduced by Lomp (1999) because of utmost importance to the topic of finite length we should be exposed of some modules which it is related to this property. In this article we introduce new conditions over semisimple, simple modules and we discuss some of the basic characterizations of these modules which show many relations between these module and length property. Since any weakly supplemented module with zero radical is semisimple then hdim(M )=length(M ) holds. Therefore supplemented and hollow modules are weakly supplemented with Rad (M )=0 implies hdim(M)=length(M ), therefore since semisimple module is direct sum of simple submodule then any simple module have finite length property.

Original languageEnglish
Title of host publicationAIP Conference Proceedings
Pages975-979
Number of pages5
Volume1571
DOIs
Publication statusPublished - 2013
Event2013 UKM Faculty of Science and Technology Post-Graduate Colloquium - Selangor
Duration: 3 Jul 20134 Jul 2013

Other

Other2013 UKM Faculty of Science and Technology Post-Graduate Colloquium
CitySelangor
Period3/7/134/7/13

Fingerprint

modules
hollow

Keywords

  • ⊕-supplemented module
  • Artinian module
  • Semisimple module
  • Simple module
  • Weakly supplemented module

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Abed, M. M., & Ahmad, A. G. (2013). Semisimple (simple) module and length property. In AIP Conference Proceedings (Vol. 1571, pp. 975-979) https://doi.org/10.1063/1.4858780

Semisimple (simple) module and length property. / Abed, Majid Mohammed; Ahmad, Abd. Ghafur.

AIP Conference Proceedings. Vol. 1571 2013. p. 975-979.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abed, MM & Ahmad, AG 2013, Semisimple (simple) module and length property. in AIP Conference Proceedings. vol. 1571, pp. 975-979, 2013 UKM Faculty of Science and Technology Post-Graduate Colloquium, Selangor, 3/7/13. https://doi.org/10.1063/1.4858780
Abed MM, Ahmad AG. Semisimple (simple) module and length property. In AIP Conference Proceedings. Vol. 1571. 2013. p. 975-979 https://doi.org/10.1063/1.4858780
Abed, Majid Mohammed ; Ahmad, Abd. Ghafur. / Semisimple (simple) module and length property. AIP Conference Proceedings. Vol. 1571 2013. pp. 975-979
@inproceedings{f6d35f2056b14116a544e14b5f76aeb3,
title = "Semisimple (simple) module and length property",
abstract = "The notion of length module was introduced by Lomp (1999) because of utmost importance to the topic of finite length we should be exposed of some modules which it is related to this property. In this article we introduce new conditions over semisimple, simple modules and we discuss some of the basic characterizations of these modules which show many relations between these module and length property. Since any weakly supplemented module with zero radical is semisimple then hdim(M )=length(M ) holds. Therefore supplemented and hollow modules are weakly supplemented with Rad (M )=0 implies hdim(M)=length(M ), therefore since semisimple module is direct sum of simple submodule then any simple module have finite length property.",
keywords = "⊕-supplemented module, Artinian module, Semisimple module, Simple module, Weakly supplemented module",
author = "Abed, {Majid Mohammed} and Ahmad, {Abd. Ghafur}",
year = "2013",
doi = "10.1063/1.4858780",
language = "English",
isbn = "9780735411999",
volume = "1571",
pages = "975--979",
booktitle = "AIP Conference Proceedings",

}

TY - GEN

T1 - Semisimple (simple) module and length property

AU - Abed, Majid Mohammed

AU - Ahmad, Abd. Ghafur

PY - 2013

Y1 - 2013

N2 - The notion of length module was introduced by Lomp (1999) because of utmost importance to the topic of finite length we should be exposed of some modules which it is related to this property. In this article we introduce new conditions over semisimple, simple modules and we discuss some of the basic characterizations of these modules which show many relations between these module and length property. Since any weakly supplemented module with zero radical is semisimple then hdim(M )=length(M ) holds. Therefore supplemented and hollow modules are weakly supplemented with Rad (M )=0 implies hdim(M)=length(M ), therefore since semisimple module is direct sum of simple submodule then any simple module have finite length property.

AB - The notion of length module was introduced by Lomp (1999) because of utmost importance to the topic of finite length we should be exposed of some modules which it is related to this property. In this article we introduce new conditions over semisimple, simple modules and we discuss some of the basic characterizations of these modules which show many relations between these module and length property. Since any weakly supplemented module with zero radical is semisimple then hdim(M )=length(M ) holds. Therefore supplemented and hollow modules are weakly supplemented with Rad (M )=0 implies hdim(M)=length(M ), therefore since semisimple module is direct sum of simple submodule then any simple module have finite length property.

KW - ⊕-supplemented module

KW - Artinian module

KW - Semisimple module

KW - Simple module

KW - Weakly supplemented module

UR - http://www.scopus.com/inward/record.url?scp=84897764966&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84897764966&partnerID=8YFLogxK

U2 - 10.1063/1.4858780

DO - 10.1063/1.4858780

M3 - Conference contribution

SN - 9780735411999

VL - 1571

SP - 975

EP - 979

BT - AIP Conference Proceedings

ER -