Finitistic Extension Degree

Details Finitistic Extension Degree Finitistic Extension Degree

2011-11-30

arxiv.org/abs/1111.7281v1

Mathematics

Commutative Algebra

Scientific paper

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.

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