Ding modules and dimensions over formal triangular matrix rings
Rendiconti del Seminario Matematico della Università di Padova, Tome 148 (2022), pp. 1-22.
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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.
DOI :
10.4171/rsmup/100
Classification :
16
@article{RSMUP_2022__148__1_0, author = {Mao, Lixin}, title = {Ding modules and dimensions over formal triangular matrix rings}, journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova}, pages = {1--22}, volume = {148}, year = {2022}, doi = {10.4171/rsmup/100}, mrnumber = {4542370}, zbl = {07673819}, language = {en}, url = {http://www.numdam.org/articles/10.4171/rsmup/100/} }
TY - JOUR AU - Mao, Lixin TI - Ding modules and dimensions over formal triangular matrix rings JO - Rendiconti del Seminario Matematico della Università di Padova PY - 2022 SP - 1 EP - 22 VL - 148 UR - http://www.numdam.org/articles/10.4171/rsmup/100/ DO - 10.4171/rsmup/100 LA - en ID - RSMUP_2022__148__1_0 ER -
Mao, Lixin. Ding modules and dimensions over formal triangular matrix rings. Rendiconti del Seminario Matematico della Università di Padova, Tome 148 (2022), pp. 1-22. doi : 10.4171/rsmup/100. http://www.numdam.org/articles/10.4171/rsmup/100/
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