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Local Unique Factorization in the Semigroup of Paths in ℝn

Published online by Cambridge University Press:  20 November 2018

Mohan S. Putcha
Mohan S. Putcha*
Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27650, U.S.A.
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Abstract

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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 22 , Issue 4 , 01 December 1979 , pp. 471 - 475
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Vol. 2 Amer. Math. Soc, Providence, R.I., 1967.Google Scholar
2. Putcha, M. S., Word equations of paths, Journal of Algebra, (accepted).Google Scholar
3. Putcha, M. S., Word equations in some geometric semigroups, Pacific Journal of Mathematics, 75 (1978) 243-266.Google Scholar