Covers and envelopes with respect to a semidualizing module

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.

Anahtar Kelimeler:

Semidualizing module, Kaplansky class, Auslander class, Bass class, (pre)envelope, (pre)cover

Covers and envelopes with respect to a semidualizing module

Keywords:

Semidualizing module, Kaplansky class, Auslander class, Bass class, (pre)envelope, (pre)cover,

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Xiaoguang YAN, Xiaosheng ZHU Department of Mathematics, Nanjing University, Nanjing 210093, P. R. CHINA e-mail: yanxg1109@gmail.com, zhuxs@nju.edu.cn