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Z_8 is not dualizable

CS. Szabo
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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 Szabó, where non-dualizability is proved for the quaternion group.

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CS. Szabo. 1997-09-06. Z_8 is not dualizable. https://arxiv.org/abs/math/9709232

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