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- W4220687101 abstract "We combine the language of monoids with the language of preorders so as to refine some fundamental aspects of the classical theory of factorization and prove an abstract factorization theorem with a variety of applications. In particular, we obtain a generalization, from cancellative to Dedekind-finite (commutative or non-commutative) monoids, of a classical theorem on “atomic factorizations” that traces back to the work of P.M. Cohn in the 1960s; recover a theorem of D.D. Anderson and S. Valdes-Leon on “irreducible factorizations” in commutative rings; improve on a theorem of A.A. Antoniou and the author that characterizes atomicity in certain “monoids of sets” naturally arising from additive number theory and arithmetic combinatorics; and give a monoid-theoretic proof that every module of finite uniform dimension over a (commutative or non-commutative) ring is a direct sum of finitely many indecomposable modules (this is in fact a special case of a more general decomposition theorem for the objects of certain categories with finite products)." @default.
- W4220687101 created "2022-04-03" @default.
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- W4220687101 date "2022-07-01" @default.
- W4220687101 modified "2023-09-23" @default.
- W4220687101 title "An abstract factorization theorem and some applications" @default.
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- W4220687101 doi "https://doi.org/10.1016/j.jalgebra.2022.03.023" @default.
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