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Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
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Nullspace of a matrix modulo an ideal
Suppose $R$ is a multivariate polynomial ring and $I$ is an ideal in $R$.
Let $M$ be a $n\times n$ square matrix with entries in $R$, and suppose that det($M$) lies in $I$.
Thus, $M$ has a non-trivia …