An investigation of the Baer–Kaplansky property
Sao Paulo Journal of Mathematical Sciences, cilt.18, sa.1, ss.121-125, 2024 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 18 Sayı: 1
- 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
- Sayfa Sayıları: ss.121-125
- 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.