Z₈ is not dualizable

1997/09/06 by Csaba Szabó, CS. Szabo, Szabo, CS.
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #math.RA

paper · pdf · doi:10.48550/arxiv.math/9709232

arxiv created 1997/09/06 · openalex publication_date 1997/09/06 · arxiv updated 2016/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we show that Z₈ does not admit a natural duality. In fact, we show that 2Z₈ = 2, 4, 6, 8 | +,. is not dualizable, and this will imply that the original ring is not dualizable, either. As a corollary we show that Sindi's conjecture does not hold. Our technique will be similar to one due to Quackenbush and Szabó, where non-dualizability is proved for the quaternion group.

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