- Turkish Journal of Mathematics
- Vol: 35 Issue: 4
- Covers and envelopes with respect to a semidualizing module
Covers and envelopes with respect to a semidualizing module
Authors : Xiaoguang Yan, Xiaosheng Zhu
Pages : 601-610
View : 11 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
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 QC by M \in QC \Leftrightarrow HomR(C,M) \in Q. We prove that if Q \subseteq (R) is a Kaplansky class and closed under direct sums, then QC\bot is special preenveloping. As corollaries, we can show that pCn \bot and fCn \bot are both special preenveloping. Finally, we show that ICn is covering, ICn \bot is enveloping and special preenveloping provided R is Noetherian.Keywords : Semidualizing module, Kaplansky class, Auslander class, Bass class, (pre)envelope, (pre)cover