Lifting properties of formal triangular matrix rings


Ozarslan M. A.

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, cilt.115, sa.3, 2021 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 115 Konu: 3
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1007/s13398-021-01044-0
  • Dergi Adı: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS

Özet

This article concerns various lifting properties of formal triangular matrix rings. The first aim is to study idempotent lifting ideals of formal triangular matrix rings. In connection with the idempotent lifting property, we also describe strong lifting, enabling and fully lifting ideals of formal triangular matrix rings. Moreover, we give a description for an ideal of a triangular matrix ring to be (idempotent) stable range one lifting. Finally, we consider other forms of lifting ideals including regular lifting, unit lifting, unit-regular lifting and clean lifting ideals for a formal triangular matrix ring, and highlight our results by providing several examples.