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Adic semidualizing complexes

School of Mathematical and Statistical Sciences, Clemson University, O-110 Martin Hall, Box 340975, Clemson, S.C. 29634, USA

E-mail Address: ssather@clemson.edu

Corresponding author.

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and

Richard Wicklein

College of Arts and Sciences, Dakota State University, 820 N Washington Ave., Madison, SD 57042, USA

E-mail Address: richard.wicklein@dsu.edu

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https://doi.org/10.1142/S021949882250089XCited by:0 (Source: Crossref)

Abstract

We introduce and study a class of objects that encompasses Christensen and Foxby’s semidualizing modules and complexes and Kubik’s quasi-dualizing modules: the class of $𝔞$ -adic semidualizing modules and complexes. We give examples and equivalent characterizations of these objects, including a characterization in terms of the more familiar semidualizing property. As an application, we give a proof of the existence of dualizing complexes over complete local rings that does not use the Cohen Structure Theorem.

Communicated by B. Olberding

Keywords:

AMSC: 13B35, 13C12, 13D09, 13D45

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