Kosmas Diveris (PhD '12)
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 generalized version of the Auslander-Reiten Conjecture for Gorenstein rings. We also examine how finitistic extension degree behaves with respect to many change of ring procedures that arise frequently in the commutative setting.
Journal: Algebras and Representation Theory
DOI: 10.1007/s10468-013-9406-2