The set of semidualizing complexes is a nontrivial metric space

JOURNAL OF ALGEBRA

卷:308

Article

Frankild, Anders ; Sather-Wagstaff, Sean

关键词: semidualizing complexes;    Gorenstein dimensions;    metric spaces;    Bass numbers;    Betti numbers;    curvature;    local homomorphisms;    Gorenstein rings;    fixed points;   

DOI  :  10.1016/j.jalgebra.2006.06.017

来源: Elsevier

【 摘 要 】

We show that the set G(R) of shift-isomorphism classes of semidualizing complexes over a local ring R admits a nontrivial metric. We investigate the interplay between the metric and several algebraic operations. Motivated by the dagger duality isometry, we prove the following: If K, L are homologically bounded below and degreewise finite R-complexes such that K circle times(L)(R) K circle times(L)(R) L is semidualizing, then K is shift-isomorphic to R. In investigating the existence of nontrivial open balls in G(R), we prove that G(R) contains elements that are not comparable in the reflexivity ordering if and only if it contains at least three distinct elements. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free