Covers and envelopes with respect to a semidualizing module

Xiaoguang YAN; Xiaosheng ZHU

Makale detayları

Covers and envelopes with respect to a semidualizing module

Yazarlar:

Xiaoguang YAN | Xiaosheng ZHU

Yayıncı:

TUBITAK

Dergi:

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

Belge Tipi:

Makale

Yayın Tarihi:

3/2011

Belge Dili:

Türkçe

Document ID (Org No.):

2000747883

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Anahtar kelimeler:

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.

 

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.

Makale detayları

Covers and envelopes with respect to a semidualizing module

Yazarlar:

Xiaoguang YAN | Xiaosheng ZHU

Yayıncı:

TUBITAK

Dergi:

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

Belge Tipi:

Makale

Yayın Tarihi:

3/2011

Belge Dili:

Türkçe

Document ID (Org No.):

2000747883

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Semidualizing module

Kaplansky class

Auslander class

Bass class

(pre)envelope

(pre)cover

Sayı

Makale detayları

Covers and envelopes with respect to a semidualizing module

Yazarlar: Xiaoguang YAN | Xiaosheng ZHU

Yayıncı: TUBITAK

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

Belge Tipi: Makale

Yayın Tarihi: 3/2011

Belge Dili: Türkçe

Document ID (Org No.): 2000747883

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Semidualizing module

Kaplansky class

Auslander class

Bass class

(pre)envelope

(pre)cover

Sayı

Yazarlar:

Xiaoguang YAN | Xiaosheng ZHU

Yayıncı:

TUBITAK

Dergi:

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

Belge Tipi:

Makale

Yayın Tarihi:

3/2011

Belge Dili:

Türkçe

Document ID (Org No.):

2000747883

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098