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Local Unique Factorization in the Semigroup of Paths in ℝn
Published online by Cambridge University Press: 20 November 2018
Abstract
Let S denote the semigroup of all rectifiable, piecewise continuously difïerentiable paths in ℝn under concatenation. We prove a theorem to the effect that every finite collection of paths is contained in a subsemigroup of S which has the unique factorization property with respect to certain primes and straight lines. We also determine an abstract necessary sufficient condition for a subsemigroup of S to have this unique factorization property.
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- Copyright © Canadian Mathematical Society 1979