On reducing homological dimensions over noetherian rings
Abstract
Let $\Lambda$ be a left and right noetherian ring. First, for $m,n\in\mathbb{N}\cup\{\infty\}$, we give equivalent conditions for a given $\Lambda$module to be $n$torsionfree and have $m$torsionfree transpose. Using them, we investigate totally reflexive modules and reducing Gorenstein dimension. Next, we introduce homological invariants for $\Lambda$modules which we call upper reducing projective and Gorenstein dimensions. We provide an inequality of upper reducing projective dimension and complexity when $\Lambda$ is commutative and local. Using it, we consider how upper reducing projective dimension relates to reducing projective dimension, and the complete intersection and AB properties of a commutative noetherian local ring.
 Publication:

arXiv eprints
 Pub Date:
 October 2020
 DOI:
 10.48550/arXiv.2010.10765
 arXiv:
 arXiv:2010.10765
 Bibcode:
 2020arXiv201010765A
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Representation Theory;
 13D05;
 13H10;
 16E10
 EPrint:
 8 pages