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math.AC2021
Bi-atomic classes of positive semirings
Nicholas R. Baeth, Scott T. Chapman, Felix Gotti
Let be a nonnegative semiring of the real line, called here a positive semiring. We study factorizations in both the additive monoid and the multiplicative monoid $(S\s…
math.AC2020
Lattices over Bass rings and graph agglomerations
Nicholas R. Baeth, Daniel Smertnig
We study direct-sum decompositions of torsion-free, finitely generated modules over a (commutative) Bass ring through the factorization theory of the corresponding monoid $T(R)…
math.AC2004
A Krull-Schmidt Theorem for One-dimensional Rings of Finite Cohen-Macaulay Type
Nicholas Baeth
We determine, up to isomorphism, the indecomposable maximal Cohen-Macaulay modules over certain complete one-dimensional local rings of finite Cohen-Macaulay type. We then investig…