Z_8 is not dualizable
Rings and Algebras
2016-09-07 v1
Abstract
In this paper we show that Z_8 does not admit a natural duality. In fact, we show that 2Z_8 = {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 Szab\'o, where non-dualizability is proved for the quaternion group.
Cite
@article{arxiv.math/9709232,
title = {Z_8 is not dualizable},
author = {CS. Szabo},
journal= {arXiv preprint arXiv:math/9709232},
year = {2016}
}