CLASSICAL ZARISKI TOPOLOGY OF MODULES AND SPECTRAL SPACES I

M. BEHBOODİ; M. R. HADDADİ

Makale detayları

CLASSICAL ZARISKI TOPOLOGY OF MODULES AND SPECTRAL SPACES I

Yazarlar:

M. BEHBOODİ | M. R. HADDADİ

Yayıncı:

Abdullah HARMANCI

Dergi:

International Electronic Journal of Algebra 2008 Vol.4 Issue 4, pp.104-130

Belge Tipi:

Makale

Yayın Tarihi:

11/2008

Belge Dili:

Türkçe

Document ID (Org No.):

2000718422

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048

Özet:

 

Let R be a ring, M be a left R-module and Spec(RM) be the collection of all prime submodules of M. In this paper and its sequel, we introduce and study a generalization of the Zariski topology of rings to modules and call it classical Zariski topology of M. Then we investigate the interplay between the module-theoretic properties of M and the topological properties of Spec(RM). Modules whose classical Zariski topology is respectively T1, Hausdorff or cofinite are studied, and several characterizations of such modules are given. We investigate this topological space from the point of view of spectral spaces (that is, topological spaces homeomorphic to the prime spectrum of a commutative ring equipped with the Zariski topology). We show that Spec(RM) is always a T0-space and each finite irreducible closed subset of Spec(RM) has a generic point. Then by applying Hochster’s characterization of a spectral space, we show that for each left R-module M with finite spectrum, Spec(RM) is a spectral space. In Part II we shall continue the study of this construction.

Makale detayları

CLASSICAL ZARISKI TOPOLOGY OF MODULES AND SPECTRAL SPACES I

Yazarlar: M. BEHBOODİ | M. R. HADDADİ

Yayıncı: Abdullah HARMANCI

Dergi: International Electronic Journal of Algebra 2008 Vol.4 Issue 4, pp.104-130

Belge Tipi: Makale

Yayın Tarihi: 11/2008

Belge Dili: Türkçe

Document ID (Org No.): 2000718422

Sıklık: Aylık

eISSN: 1306-6048

pISSN: 1306-6048

Sayı

Yazarlar:

M. BEHBOODİ | M. R. HADDADİ

Yayıncı:

Abdullah HARMANCI

Dergi:

International Electronic Journal of Algebra 2008 Vol.4 Issue 4, pp.104-130

Belge Tipi:

Makale

Yayın Tarihi:

11/2008

Belge Dili:

Türkçe

Document ID (Org No.):

2000718422

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048