Degree-one cup-square obstruction to ring isomorphism
= Degree-one cup-square obstruction to ring isomorphism
{title2=$z\in H^1,\quad z^2\ne0$}
The property that every degree-one element has square zero is invariant under a graded ring isomorphism. Over $\mathbb F_2$ it distinguishes the <cohomology ring of a torus> from the <mod-two cohomology ring of an inversion mapping torus> of dimension at least two.