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

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The center of a(n endomorphism) ring is a PID

Here are two results from the literature, found in Endomorphism Rings of Abelian Groups, p. 269. For these to be relevant, we need $\mathrm{End}(A)$ to be commutative. Some terminology. A group is $A …
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