Abstract
For convex sets, in particular convex cones and polyhedra, as well as for commutative monoids, in particular the multiplicative semi-groups of integral domains, a method of marked extraction is outlined. By this method, elements can be represented uniquely by distinguished elements such as extreme points and irreducible elements, respectively, if some marking is employed. Geometrically, this yields a particular simplicial subdivision of convex sets and monoids, respectively. Applied to the topic of joint production from economics the famous Nonsubstitution Theorem is generalized to a Substitution Theorem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
S.T. Chapman, U. Krause, and E. Oeljeklaus, Monoids determined by a homogeneous linear diophantine equation and the half-factorial property, J. Pure Appl. Algebra, 2000 (to appear).
F. Halter-Koch, Ideal Systems. An Introduction to Multiplicative Ideal Theory, M. Dekker Inc., New York, 1998.
D. Hinrichsen and U. Krause, Choice of techniques in joint production models, Operations Research Verfahren 34:155–171, 1971.
D. Hinrichsen and U. Krause, A substitution theorem for joint production models with disposal processes, Operations Research Verfahren 41:287–291,1981.
D. Hinrichsen and U. Krause, Unique representation in convex sets by extraction of marked components, Linear Algebra Appl. 51:73–96, 1983.
U. Krause, Eindeutige Faktorisierung ohne ideale Elemente, Abh. Braunschw. Wiss. Ges. (Dedekind Festschrift) 33:169–177, 1982.
U. Krause, On monoids of finite real character, Proc. Am. Math. Soc. 105:546–554,1989.
U. Krause, Semigroups that are factorial from inside or from outside, in J. Almeida et al., eds., Lattices, Semigroups, and Universal Algebra, 147–161, Plenum, New York, 1990.
U. Krause, Positive nonlinear systems: Some results and applications, in V. Lakshmikantham, ed., Proc. 1st World Congress of Nonlinear Analysts, 1529–1539, de Gruyter, Berlin, 1996.
H.D. Kurz and N. Salvadori, Theory of Production. A Long-Period Analysis, Cambridge University Press, Cambridge, 1995.
H. Matsumura, Commutative Ring Theory, Cambridge University Press, Cambridge, 1986.
M. Morishima, Equilibrium, Stability, and Growth. A Multi-Sectoral Analysis, Oxford University Press, London, 1964.
J. von Neumann, A model of general economic equilibrium, Rev. Econ. Studies 13:1–9, 1945 (originally published in German 1937).
R.T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, 1970.
H. Wistuba, Faktorielle Komplexe, Ph.D.thesis, University of Bremen, 1991.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media New York
About this chapter
Cite this chapter
Krause, U. (2001). A General Principle of Marked Extraction. In: Colonius, F., Helmke, U., Prätzel-Wolters, D., Wirth, F. (eds) Advances in Mathematical Systems Theory. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0179-3_10
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0179-3_10
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6649-5
Online ISBN: 978-1-4612-0179-3
eBook Packages: Springer Book Archive