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math.AC2003
Bounds and definability in polynomial rings
Matthias Aschenbrenner
We study questions around the existence of bounds and the dependence on parameters for linear-algebraic problems in polynomial rings over rings of an arithmetic flavor.In particula…
math.AC2003★ 4 cited
Ideal Membership in Polynomial Rings over the Integers
Matthias Aschenbrenner
We present a new approach to the ideal membership problem for polynomial rings over the integers: given polynomials , where is an -tup…
math.LO2003
Orderings of Monomial Ideals
Matthias Aschenbrenner, Wai-Yan Pong
We study the set of monomial ideals in a polynomial ring as an ordered set, with the ordering given by reverse inclusion. We give a short proof of the fact that every antichain of…