Homology with the theme of Matlis
Commutative Algebra
2023-02-15 v2
Abstract
Matlis proved a lot of homological properties of the fraction field of an integral domain. In this paper, we simplify and extend some of them from 1-dimensional (resp. rank one) cases to the higher dimensional (resp. finite rank) cases. For example, we study the weakly co-torsion property of Ext, and use it to present splitting criteria. These are equipped with several applications. For instance, we compute the projective dimension of and present some non-noetherian versions of Grothendieck's localization problem. We construct a new class of co-Hopfian modules and extend Matlis' decomposability problem to higher ranks. In particular, this paper deals with the basic properties of Matlis' quadric
Keywords
Cite
@article{arxiv.2212.10332,
title = {Homology with the theme of Matlis},
author = {Mohsen Asgharzadeh and Elham Mahdavi},
journal= {arXiv preprint arXiv:2212.10332},
year = {2023}
}