Journals / Turkish Journal of Mathematics / 2011 / Cilt: 35 - Sayı: 4
Covers and envelopes with respect to a semidualizing module
- Pages
- 601–610
- DOI
- —
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.
Özet
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.