Finitistic Extension Degree
Commutative Algebra
2013-09-05 v2
Abstract
We introduce the finitistic extension degree of a ring and investigate rings for which it is finite. The Auslander-Reiten Conjecture is proved for rings of finite finitistic extension degree and these rings are also shown to have finite finitistic dimension. We apply these results to better understand a gen- eralized version of the Auslander-Reiten Condition for Gorenstein rings. We also record how the finitistic extension degree behaves with respect to many change of ring procedures that arise frequently in the commutative setting.
Cite
@article{arxiv.1111.7281,
title = {Finitistic Extension Degree},
author = {Kosmas Diveris},
journal= {arXiv preprint arXiv:1111.7281},
year = {2013}
}