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October, 2021 On $n$-phantom and $n$-Ext-phantom Morphisms
Kaiyang Lan, Bo Lu
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Taiwanese J. Math. 25(5): 941-957 (October, 2021). DOI: 10.11650/tjm/210306


This paper extends many conclusions based on phantom envelopes and Ext-phantom covers of modules, and we find that many important properties still hold after replacing phantom and Ext-phantom with $n$-phantom and $n$-Ext-phantom respectively. In addition, we also obtain some extra results. Specifically, we give a characterization of the weak dimensions of rings in terms of $n$-phantom envelopes and $n$-Ext-phantom covers of modules with the unique mapping property respectively. We show that $\operatorname{wD}(R) \leq 2n$ whenever every right $R$-module has an $n$-phantom envelope with the unique mapping property or every left $R$-module has an $n$-Ext-phantom cover with the unique mapping property over left coherent rings.

Funding Statement

This work was supported by National Natural Science Foundation of China (No. 12061061), Fundamental Research Funds for the Central Universities (No. 31920190057) and Innovation Team Project of Northwest Minzu University (No. 1110130131).


Download Citation

Kaiyang Lan. Bo Lu. "On $n$-phantom and $n$-Ext-phantom Morphisms." Taiwanese J. Math. 25 (5) 941 - 957, October, 2021.


Received: 11 August 2020; Revised: 12 March 2021; Accepted: 21 March 2021; Published: October, 2021
First available in Project Euclid: 24 March 2021

Digital Object Identifier: 10.11650/tjm/210306

Primary: 16D90, 16E30, 18G25

Rights: Copyright © 2021 The Mathematical Society of the Republic of China


Vol.25 • No. 5 • October, 2021
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