Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
HOMOLOGICAL DIMENSIONS IN COTORSION PAIRS LIDIA ANGELERI HUGEL AND OCTAVIO MENDOZA
 

Summary: HOMOLOGICAL DIMENSIONS IN COTORSION PAIRS
LIDIA ANGELERI H¨UGEL AND OCTAVIO MENDOZA
Abstract. Two classes A and B of modules over a ring R are said to form
a cotorsion pair (A, B) if A = Ker Ext1
R(-, B) and B = Ker Ext1
R(A, -). We
investigate relative homological dimensions in cotorsion pairs. This can be
applied to study the big and the little finitistic dimension of R. We show
that Findim R < if and only if the following dimensions are finite for some
cotorsion pair (A, B) in Mod R: the relative projective dimension of A with
respect to itself, and the A-resolution dimension of the category P of all R-
modules of finite projective dimension. Moreover, we obtain an analogous
result for findim R, and we characterize when Findim R = findim R.
Introduction.
The study of homological dimensions which are obtained by replacing the pro-
jective or injective modules by certain subcategories was initiated by Auslander and
Buchweitz in their seminal paper [5], which was one of the starting points for what
is now called relative homological algebra.
Of course, the existence of approximations is the prerequisite for computing
relative dimensions. In recent years, a powerful machinery for producing approxi-

  

Source: Angeleri Hügel, Lidia - Dipartimento di Informatica, Universita` di Verona

 

Collections: Mathematics