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Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
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Decomposition of finitely generated algebras
As I cannot mark a comment as an answer, I'll follow the ideas of YCor and Benjamin Steinberg to answer this question.
Let $A$ an arbitrary noetherian ring, then the boolean algebra of idempotents of …
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Decomposition of finitely generated algebras
Let $k$ be a field and $A$ a finitely generated algebra over $k$. I know that if $A$ is finite dimensional as a vector space over $k$, then $A$ can be decomposed as a product of indecomposable $k$-alg …