Rings for which every cosingular module is discrete

Yahya TALEBİ; Ali Reza MONİRİ HAMZEKOLAEE; Abdullah HARMANCI; Burcu ÜNGÖR

doi:https://doi.org/10.15672/hujms.500759

Makale detayları

Rings for which every cosingular module is discrete

Yazarlar:

Yahya TALEBİ | Ali Reza MONİRİ HAMZEKOLAEE | Abdullah HARMANCI | Burcu ÜNGÖR

Yayıncı:

Hacettepe University

Ana Başlıklar:

Matematik

Dergi:

Hacettepe Journal of Mathematics and Statistics 2020 Vol.49 Issue 5, pp.1635-1648

Belge Tipi:

Makale

Yayın Tarihi:

10/2020

Belge Dili:

İngilizce

Document ID (Org No.):

2000450919

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X

DOI:

https://doi.org/10.15672/hujms.500759

Özet:

 

In this paper we introduce the concepts of CDCDCD-rings and CDCDCD-modules. Let RRR be a ring and MMM be an RRR-module. We call RRR a CDCDCD-ring in case every cosingular RRR-module  is discrete, and MMM a CDCDCD-module if every MMM-cosingular RRR-module in σ[M]σ[M]\sigma[M] is discrete. If RRR is a ring such that the class of cosingular RRR-modules is closed under factor modules, then it is proved that RRR is a CDCDCD-ring if and only if every cosingular RRR-module is semisimple. The relations of CDCDCD-rings are investigated with VVV-rings, GVGVGV-rings, SCSCSC-rings, and rings with all cosingular RRR-modules projective. If RRR is a semilocal ring, then it is shown that RRR is right CDCDCD if and only if RRR is left SCSCSC with Soc(RR)Soc(RR)Soc(_{R}R) essential in RRRR_{R}R. Also, being a VVV-ring and being a CDCDCD-ring coincide for local rings. Besides of these, we characterize CDCDCD-modules with finite hollow dimension.

Makale detayları

Rings for which every cosingular module is discrete

Yazarlar: Yahya TALEBİ | Ali Reza MONİRİ HAMZEKOLAEE | Abdullah HARMANCI | Burcu ÜNGÖR

Yayıncı: Hacettepe University

Ana Başlıklar: Matematik

Dergi: Hacettepe Journal of Mathematics and Statistics 2020 Vol.49 Issue 5, pp.1635-1648

Belge Tipi: Makale

Yayın Tarihi: 10/2020

Belge Dili: İngilizce

Document ID (Org No.): 2000450919

Sıklık: İki Aylık

eISSN: 2651-477X

pISSN: 2651-477X

DOI: https://doi.org/10.15672/hujms.500759

Sayı

Yazarlar:

Yahya TALEBİ | Ali Reza MONİRİ HAMZEKOLAEE | Abdullah HARMANCI | Burcu ÜNGÖR

Yayıncı:

Hacettepe University

Ana Başlıklar:

Matematik

Dergi:

Hacettepe Journal of Mathematics and Statistics 2020 Vol.49 Issue 5, pp.1635-1648

Belge Tipi:

Makale

Yayın Tarihi:

10/2020

Belge Dili:

İngilizce

Document ID (Org No.):

2000450919

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X

DOI:

https://doi.org/10.15672/hujms.500759