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Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.

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Alternating forms on abelian groups

The answer is no. I give an example with a rank $3$ torsion-free abelian group $L$. We have the alternating map$$L \times L \to \wedge^2 L, \quad x \otimes y \mapsto x \wedge y.$$We have the alternati …
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