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, XIAOGUANG and ZHU, XIAOSHENG
(2011)
"Covers and envelopes with respect to a semidualizing module,"
Turkish Journal of Mathematics: Vol. 35:
No.
4, Article 1.
https://doi.org/10.3906/mat-1009-1
Available at:
https://journals.tubitak.gov.tr/math/vol35/iss4/1
