Covers and envelopes with respect to a semidualizing module

Xiaoguang YAN; Xiaosheng ZHU

Article Details

Covers and envelopes with respect to a semidualizing module

Authors:

Xiaoguang YAN | Xiaosheng ZHU

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2011 Vol.35 Issue 4, pp.601-610

Document Type:

Article

Publication Date:

3/2011

Document Language:

Turkish

Document ID (Org No.):

2000747883

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

Keywords:

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.

 

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.

Article Details

Covers and envelopes with respect to a semidualizing module

Authors:

Xiaoguang YAN | Xiaosheng ZHU

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2011 Vol.35 Issue 4, pp.601-610

Document Type:

Article

Publication Date:

3/2011

Document Language:

Turkish

Document ID (Org No.):

2000747883

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

Semidualizing module

Kaplansky class

Auslander class

Bass class

(pre)envelope

(pre)cover

Issues

Article Details

Covers and envelopes with respect to a semidualizing module

Authors: Xiaoguang YAN | Xiaosheng ZHU

Publisher: TUBITAK

Journal: Turkish Journal of Mathematics 2011 Vol.35 Issue 4, pp.601-610

Document Type: Article

Publication Date: 3/2011

Document Language: Turkish

Document ID (Org No.): 2000747883

Frequency: Bimonthly

eISSN: 1303-6149

pISSN: 1300-0098

Semidualizing module

Kaplansky class

Auslander class

Bass class

(pre)envelope

(pre)cover

Issues

Authors:

Xiaoguang YAN | Xiaosheng ZHU

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2011 Vol.35 Issue 4, pp.601-610

Document Type:

Article

Publication Date:

3/2011

Document Language:

Turkish

Document ID (Org No.):

2000747883

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098