Abstract
<abstract><p>Let $ R, S $ be arbitrary associative rings and $ _RC_S $ a semidualizing bimodule. We give some equivalent characterizations for $ R $ being left coherent (and right perfect) rings, left Noetherian rings and left Artinian rings in terms of the $ C $-($ {\mathop{{{\text{FP}}}}\nolimits} $-)injectivity, flatness and projectivity of character modules of certain left $ S $-modules.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference28 articles.
1. T. J. Cheatham, D. R. Stone, Flat and projective character modules, Proc. Amer. Math. Soc., 81 (1981), 175–177. https://doi.org/10.1090/S0002-9939-1981-0593450-2
2. E. E. Enochs, O. M. G. Jenda, Relative Homological Algebra, Vol. 1, the second revised and extended edition, de Gruyter Expositions in Math, Walter de Gruyter GmbH & Co. KG, Berlin, 2011. https://doi.org/10.1515/9783110215212
3. D. J. Fieldhouse, Character modules, Comment. Math. Helv., 46 (1971), 274–276. https://doi.org/10.1007/BF02566844
4. R. Göbel, J. Trlifaj, Approximations and Endomorphism Algebras of Modules, Second revised and extended edition, Walter de Gruyter GmbH & Co. KG, Berlin, 2012. https://doi.org/10.1515/9783110218114
5. Z. Y. Huang, Duality pairs induced by Auslander and Bass classes, Georgian Math. J., 28 (2021), 867–882. https://doi.org/10.1515/gmj-2021-2101