An Example of an Indecomposable Module Without Non-Zero Hollow Factor Modules

Christian LOMP

Makale detayları

An Example of an Indecomposable Module Without Non-Zero Hollow Factor Modules

Yazarlar:

Christian LOMP

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2007 Vol.31 Issue 4, pp.415-419

Belge Tipi:

Makale

Yayın Tarihi:

3/2007

Belge Dili:

Türkçe

Document ID (Org No.):

2000748403

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Anahtar kelimeler:

Özet:

 

A module M is called hollow-lifting if every submodule N of  M such that M/N is hollow contains a direct summand D \subseteq N such  that N/D is a small submodule of M/D. A module M is called lifting if  such a direct summand D exists for every submodule N. We construct an  indecomposable module M without non-zero hollow factor modules,  showing that there are hollow-lifting modules which are not lifting.   The existences of such modules had been left open in a recent work by  N. Orhan, D. Keskin-Tütüncü and R. Tribak [2].

 

A module M is called hollow-lifting if every submodule N of  M such that M/N is hollow contains a direct summand D \subseteq N such  that N/D is a small submodule of M/D. A module M is called lifting if  such a direct summand D exists for every submodule N. We construct an  indecomposable module M without non-zero hollow factor modules,  showing that there are hollow-lifting modules which are not lifting.   The existences of such modules had been left open in a recent work by  N. Orhan, D. Keskin-Tütüncü and R. Tribak [2].

Makale detayları

An Example of an Indecomposable Module Without Non-Zero Hollow Factor Modules

Yazarlar:

Christian LOMP

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2007 Vol.31 Issue 4, pp.415-419

Belge Tipi:

Makale

Yayın Tarihi:

3/2007

Belge Dili:

Türkçe

Document ID (Org No.):

2000748403

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Hollow modules

Indecomposable modules

Lifting modules

coalgebras

Sayı

Makale detayları

An Example of an Indecomposable Module Without Non-Zero Hollow Factor Modules

Yazarlar: Christian LOMP

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2007 Vol.31 Issue 4, pp.415-419

Belge Tipi: Makale

Yayın Tarihi: 3/2007

Belge Dili: Türkçe

Document ID (Org No.): 2000748403

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Hollow modules

Indecomposable modules

Lifting modules

coalgebras

Sayı

Yazarlar:

Christian LOMP

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2007 Vol.31 Issue 4, pp.415-419

Belge Tipi:

Makale

Yayın Tarihi:

3/2007

Belge Dili:

Türkçe

Document ID (Org No.):

2000748403

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098