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 T = A 0 U B be a formal triangular matrix ring, where A and B are rings and U is a (B,A)-bimodule. We prove: (1) If U A and B U have finite flat dimensions, then a left T-module M 1 M 2 φ M is Ding projective if and only if M 1 and M 2 /im(φ M ) are Ding projective and the morphism φ M is a monomorphism. (2) If T is a right coherent ring, B U has finite flat dimension, U A is finitely presented and has finite projective or FP-injective dimension, then a right T-module (W 1 ,W 2 ) φ W is Ding injective if and only if W 1 and ker(φ W ˜) are Ding injective and the morphism φ W ˜ is an epimorphism. As a consequence, we describe Ding projective and Ding injective dimensions of a T-module.

DOI : 10.4171/rsmup/100
Classification : 16
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     author = {Lixin Mao},
     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},
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     language = {en},
     url = {http://www.numdam.org/articles/10.4171/rsmup/100/}
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Lixin Mao. 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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