Quasi regular modules and trivial extension

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Jayaram C., TEKİR Ü., KOÇ S.

Hacettepe Journal of Mathematics and Statistics, cilt.50, sa.1, ss.120-134, 2021 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 50 Sayı: 1
  • Basım Tarihi: 2021
  • Doi Numarası: 10.15672/hujms.613404
  • Dergi Adı: Hacettepe Journal of Mathematics and Statistics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.120-134
  • Anahtar Kelimeler: von Neumann regular ring, quasi regular ring, von Neumann regular module, quasi regular module, trivial extension
  • Marmara Üniversitesi Adresli: Evet

Özet

© 2021, Hacettepe University. All rights reserved.Recall that a ring R is said to be a quasi regular ring if its total quotient ring q(R) is von Neumann regular. It is well known that a ring R is quasi regular if and only if it is a reduced ring satisfying the property: for each a ∈ R, annR(annR(a)) = annR(b) for some b ∈ R. Here, in this study, we extend the notion of quasi regular rings and rings which satisfy the aforementioned property to modules. We give many characterizations and properties of these two classes of modules. Moreover, we investigate the (weak) quasi regular property of trivial extension.