Ding modules and dimensions over formal triangular matrix rings

  • Lixin Mao

    Nanjing Institute of Technology, China
Ding modules and dimensions over formal triangular matrix rings cover

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Abstract

Let be a formal triangular matrix ring, where and are rings and is a -bimodule. We prove: (1) If and have finite flat dimensions, then a left -module is Ding projective if and only if and are Ding projective and the morphism is a monomorphism. (2) If is a right coherent ring, has finite flat dimension, is finitely presented and has finite projective or -injective dimension, then a right -module is Ding injective if and only if and are Ding injective and the morphism is an epimorphism. As a consequence, we describe Ding projective and Ding injective dimensions of a -module.

Cite this article

Lixin Mao, Ding modules and dimensions over formal triangular matrix rings. Rend. Sem. Mat. Univ. Padova 148 (2022), pp. 1–22

DOI 10.4171/RSMUP/100