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Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.
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Smith Normal Form and lower triangular Toeplitz Matrices
Some friends (including the original poster!) and I wrote up the proof of the result in this paper. The proof involves symmetric function theory.