An investigation of the Baer–Kaplansky property

KESKİN TÜTÜNCÜ D., Başer Z.

Sao Paulo Journal of Mathematical Sciences, 2024 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s40863-024-00407-w
  • Dergi Adı: Sao Paulo Journal of Mathematical Sciences
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Anahtar Kelimeler: Artin ring, Baer–Kaplansky class, Local ring, Perfect ring, Primary: 16D10, Secondary: 16L30
  • Hacettepe Üniversitesi Adresli: Evet

Özet

In this paper, we construct a local artinian ring R with Jacobson radical W such that W2=0, Q=R/W is commutative, dim(QW)=1 and dim(WQ)=2. Then we show that, for this ring R, the category of all right R-modules Mod-R is not a Baer–Kaplansky class by proving that the class of all indecomposable right R-modules (all finitely generated right R-modules) is not Baer-Kaplansky. Finally, we give an application on some module classes over this constructed ring R.