SOME PROPERTIES OF RICKART MODULES
Yıl: 2012 Cilt: 61 Sayı: 2 Sayfa Aralığı: 1 - 8 Metin Dili: Türkçe İndeks Tarihi: 29-07-2022
SOME PROPERTIES OF RICKART MODULES
Öz: 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¸llerin zellikleriincelenmeyedevamedilmi?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 g sterilmi?stir. M[x], S[x] halkas¨na g re 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.
Anahtar Kelime: Konular:
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Öz: 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.
Anahtar Kelime: Konular:
Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
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APA | Ungor B, KAFKAS G, HALICIOGLU S, Harmanci A (2012). SOME PROPERTIES OF RICKART MODULES. , 1 - 8. |
Chicago | Ungor Burcu,KAFKAS Gizem,HALICIOGLU Salt,Harmanci Abdullah SOME PROPERTIES OF RICKART MODULES. (2012): 1 - 8. |
MLA | Ungor Burcu,KAFKAS Gizem,HALICIOGLU Salt,Harmanci Abdullah SOME PROPERTIES OF RICKART MODULES. , 2012, ss.1 - 8. |
AMA | Ungor B,KAFKAS G,HALICIOGLU S,Harmanci A SOME PROPERTIES OF RICKART MODULES. . 2012; 1 - 8. |
Vancouver | Ungor B,KAFKAS G,HALICIOGLU S,Harmanci A SOME PROPERTIES OF RICKART MODULES. . 2012; 1 - 8. |
IEEE | Ungor B,KAFKAS G,HALICIOGLU S,Harmanci A "SOME PROPERTIES OF RICKART MODULES." , ss.1 - 8, 2012. |
ISNAD | Ungor, Burcu vd. "SOME PROPERTIES OF RICKART MODULES". (2012), 1-8. |
APA | Ungor B, KAFKAS G, HALICIOGLU S, Harmanci A (2012). SOME PROPERTIES OF RICKART MODULES. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 61(2), 1 - 8. |
Chicago | Ungor Burcu,KAFKAS Gizem,HALICIOGLU Salt,Harmanci Abdullah SOME PROPERTIES OF RICKART MODULES. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 61, no.2 (2012): 1 - 8. |
MLA | Ungor Burcu,KAFKAS Gizem,HALICIOGLU Salt,Harmanci Abdullah SOME PROPERTIES OF RICKART MODULES. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, vol.61, no.2, 2012, ss.1 - 8. |
AMA | Ungor B,KAFKAS G,HALICIOGLU S,Harmanci A SOME PROPERTIES OF RICKART MODULES. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2012; 61(2): 1 - 8. |
Vancouver | Ungor B,KAFKAS G,HALICIOGLU S,Harmanci A SOME PROPERTIES OF RICKART MODULES. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2012; 61(2): 1 - 8. |
IEEE | Ungor B,KAFKAS G,HALICIOGLU S,Harmanci A "SOME PROPERTIES OF RICKART MODULES." Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 61, ss.1 - 8, 2012. |
ISNAD | Ungor, Burcu vd. "SOME PROPERTIES OF RICKART MODULES". Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 61/2 (2012), 1-8. |