Geodesic
Local Unique Factorization in the Semigroup of Paths in Rn
Canadian mathematical bulletin, Tome 22 (1979) no. 4, pp. 471-475

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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. 
Putcha, Mohan S. Local Unique Factorization in the Semigroup of Paths in Rn. Canadian mathematical bulletin, Tome 22 (1979) no. 4, pp. 471-475. doi: 10.4153/CMB-1979-061-6
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     title = {Local {Unique} {Factorization} in the {Semigroup} of {Paths} in {Rn}},
     journal = {Canadian mathematical bulletin},
     pages = {471--475},
     year = {1979},
     volume = {22},
     number = {4},
     doi = {10.4153/CMB-1979-061-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1979-061-6/}
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