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Elasticity in orders of an algebraic number field with radical conductor ideal and their rings of formal power series
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Orders in an algebraic number field form a class of rings which are of special historical interest to the field of factorization theory. One of the primary tools used to study factorization is elasticity - a measure of how badly unique factorization fails in a domain. This paper explores properties of orders in a number field and how they can be used to study elasticity in not only the orders themselves, but also in rings of formal power series over the orders. Of particular interest is the fact, proven here, that power series extensions in finitely many variables over half-factorial rings of algebraic integers must themselves be half-factorial. It is also shown that the HFD property is not preserved in general for power series rings over non-integrally closed orders in a number field.
Forward citations
Cited by 3 Pith papers
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Elasticity of Orders from the $S$-relative Davenport Constant: an Arithmetic Application of a Number-Theoretic Investigation
Exact elasticity formulas for orders with prime or primary conductor are proven via a new S-relative Davenport constant, with a partial resolution of the intermediate-order elasticity conjecture.
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(Locally) Associated Subrings in Polynomial and Power Series Extensions
Full necessary-and-sufficient conditions are given for coefficient-varying polynomial and power series rings to be (locally) associated subrings of larger such rings, with consequences for half-factorial power series ...
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On $q$-real and $q$-complex numbers
For every real x > 1 the q-real series [x]_q converges in the disk |q| < 3−2√2 to a nonvanishing holomorphic function, partially proving the radius-convergence conjecture.
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