## Illinois Journal of Mathematics

### On the structure of the set of semidualizing complexes

A. Gerko

#### Abstract

We study the structure of the set of semidualizing complexes over a local ring. In particular, we prove that for a pair of semidualizing complexes $X_1$ and $X_2$ such that $G_{X_{2}}\dim X_{1}<\infty$ we have $X_2\simeq X_1\otimes^{L}_R\func{\mathbf{R}Hom}_R(X_{1},X_{2})$. Specializing to the case of semidualizing modules over artinian rings we obtain a number of quantitative results for rings possessing a configuration of semidualizing modules of special form. For rings with ${\mathfrak m}^3=0$ this condition reduces to the existence of a nontrivial semidualizing module and we prove a number of structural results in this case.

#### Article information

Source
Illinois J. Math., Volume 48, Number 3 (2004), 965-976.

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258131064

Digital Object Identifier
doi:10.1215/ijm/1258131064

Mathematical Reviews number (MathSciNet)
MR2114263

Zentralblatt MATH identifier
1080.13009

Subjects
Primary: 13D25

#### Citation

Gerko, A. On the structure of the set of semidualizing complexes. Illinois J. Math. 48 (2004), no. 3, 965--976. doi:10.1215/ijm/1258131064. https://projecteuclid.org/euclid.ijm/1258131064