Homology with respect to a kernel transformation

Seyed Naser HOSSEINI; Mohammad Zaher Kazemi BANEH

Makale detayları

Homology with respect to a kernel transformation

Yazarlar:

Seyed Naser HOSSEINI | Mohammad Zaher Kazemi BANEH

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2011 Vol.35 Issue 2, pp.169-186

Belge Tipi:

Makale

Yayın Tarihi:

1/2011

Belge Dili:

Türkçe

Document ID (Org No.):

2000747963

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Anahtar kelimeler:

Özet:

 

In this article we first give the relations between commonly  used images of a morphism in a category.  We then investigate  d-homology in a category with certain properties, for a kernel  transformation d.  In particular, we show that, in an abelian  category, d-homology, where d is induced by the subtraction operation,  is the standard homology and that in more general categories the  d-homology for a trivial d is zero.  We also compute through examples  the d-homology for certain kernel transformations d in such categories  as R-modules, abelian groups and short exact sequences of R-modules.  Finally, we characterize kernel transformations in the categories of  R-modules, finitely generated R-modules, partial sets and pointed  sets.

 

In this article we first give the relations between commonly  used images of a morphism in a category.  We then investigate  d-homology in a category with certain properties, for a kernel  transformation d.  In particular, we show that, in an abelian  category, d-homology, where d is induced by the subtraction operation,  is the standard homology and that in more general categories the  d-homology for a trivial d is zero.  We also compute through examples  the d-homology for certain kernel transformations d in such categories  as R-modules, abelian groups and short exact sequences of R-modules.  Finally, we characterize kernel transformations in the categories of  R-modules, finitely generated R-modules, partial sets and pointed  sets.

Makale detayları

Homology with respect to a kernel transformation

Yazarlar:

Seyed Naser HOSSEINI | Mohammad Zaher Kazemi BANEH

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2011 Vol.35 Issue 2, pp.169-186

Belge Tipi:

Makale

Yayın Tarihi:

1/2011

Belge Dili:

Türkçe

Document ID (Org No.):

2000747963

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Kernel

image

abelian category

standard homology

homology with respect to a kernel transformation

category of (finitely generated) R-modules

(finitely generated) abelian groups

partial sets

pointed sets

Sayı

Makale detayları

Yazarlar: Seyed Naser HOSSEINI | Mohammad Zaher Kazemi BANEH

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2011 Vol.35 Issue 2, pp.169-186

Belge Tipi: Makale

Yayın Tarihi: 1/2011

Belge Dili: Türkçe

Document ID (Org No.): 2000747963

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Seyed Naser HOSSEINI | Mohammad Zaher Kazemi BANEH

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2011 Vol.35 Issue 2, pp.169-186

Belge Tipi:

Makale

Yayın Tarihi:

1/2011

Belge Dili:

Türkçe

Document ID (Org No.):

2000747963

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098