Turkish Journal of Mathematics
Abstract
Let R be a commutative ring and C be a semidualizing R-module. For a given class of R-modules Q, we define a class Q_C by M \in Q_C \Leftrightarrow Hom_R(C,M) \in Q. We prove that if Q \subseteq (R) is a Kaplansky class and closed under direct sums, then Q_C^{\bot} is special preenveloping. As corollaries, we can show that p_C^{n \bot} and f_C^{n \bot} are both special preenveloping. Finally, we show that I_C^n is covering, I_C^{n \bot} is enveloping and special preenveloping provided R is Noetherian.
DOI
10.3906/mat-1009-1
Keywords
Semidualizing module, Kaplansky class, Auslander class, Bass class, (pre)envelope, (pre)cover
First Page
601
Last Page
610
Recommended Citation
YAN, X, & ZHU, X (2011). Covers and envelopes with respect to a semidualizing module. Turkish Journal of Mathematics 35 (4): 601-610. https://doi.org/10.3906/mat-1009-1
