Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/10298
Title: Some Properties of Rickart Modules
Authors: Üngör, Burcu
Kafkas, Gizem
Halıcıoğlu, Sait
Harmancı, Abdullah
Keywords: Symmetric modules
Rickart modules
Reduced modules
Publisher: Ankara Üniversitesi
Abstract: R birimli bir halka, M saº g R-mod¸l ve M nin endomorÖzma halkas¨ S = EndR(M) olsun. Her f 2 S iÁin rM(f) = eM olacak biÁimde e2 = e 2 S varsa (denk olarakKerf,Mmod¸l¸n¸nbirdirekttoplanan¨ise)MyeRickartmod¸lad¨verilmi?stir[8]. BuÁal¨?smadaRickartmod¸llerinˆzellikleriincelenmeyedevamedilmi?stir. M birRickart mod¸l olmak ¸zere, M nin S-kat¨ (s¨ras¨yla S-indirgenmi?s, S-simetrik, S-yar¨ deºgi?smeli, S-Armendariz)mod¸l olmas¨ iÁin gerek ve yeter ?sart¨n S nin kat¨ (s¨ras¨yla indirgenmi?s, simetrik, yar¨ deºgi?smeli, Armendariz) halka olduºgu gˆsterilmi?stir. M[x], S[x] halkas¨na gˆre Rickart mod¸l iken M nin de Rickart mod¸l oldugu,tersinin M nin S-Armendariz olmas¨ durumunda doºgru olduºgu ispatlanm¨?st¨r. Ayrıca bir M mod¸l¸n¸n Rickart ol- mas¨iÁingerekveyeter?sart¨nhersaºgmod¸l¸nM-temelprojektifolduºgueldeedilmi?stir.
Let Rbeanarbitraryringwithidentity and M aright R-module with S =EndR(M). Following [8],the module M is called Rickart if for any f 2 S, rM(f) = eM for some e2 = e 2 S, equivalently, Kerf is a direct summandofM. Inthispaper,wecontinuetoinvestigatepropertiesofRickart modules. For a Rickart module M, we prove that M is S-rigid (resp., S- reduced, S-symmetric, S-semicommutative, S-Armendariz) if and only if its endomorphism ring S is rigid (resp., reduced, symmetric, semicommutative, Armendariz). We also prove that if M[x]is a Rickart module with respect to S[x], then M is Rickart, the converse holds if M is S-Armendariz. Among others it is also shown that M is a Rickart module if and only if every right R-module is M-principally projective.
URI: https://hdl.handle.net/11147/10298
https://doi.org/10.1501/Commua1_0000000675
ISSN: 1303-5991
2618-6470
Appears in Collections:Mathematics / Matematik
TR Dizin İndeksli Yayınlar / TR Dizin Indexed Publications Collection

Files in This Item:
File SizeFormat 
2e5f7003-44da-4014-b802-f559945f8d78.pdf141.18 kBAdobe PDFView/Open
Show full item record



CORE Recommender

Page view(s)

446
checked on Dec 23, 2024

Download(s)

86
checked on Dec 23, 2024

Google ScholarTM

Check





Items in GCRIS Repository are protected by copyright, with all rights reserved, unless otherwise indicated.