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Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
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What can be said about $A$ and $B$ given the exact sequence $0 \to R^p \to A \to R^r \to R^q...
Let $A,B$ be two $R$-modules over a commutative ring $R$ (restrict to $R = \mathbb{Z}$ or $R= \mathbb{K}$ a field where appropriate). Suppose $A$ and $B$ fit into an exact sequence
$0 \to R^p \to …