REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, vol.115, no.3, 2021 (SCI-Expanded)
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.