The Quillen-Suslin Theorem and the Structure of n-Dimensional Elementary Polynomial Matrices

IEEE Transactions on Circuits and Systems

Volumn 31, Issue 6, 1984, Pages 513-518

  Youla, D C ^a   Pickel, P F ^a  

^a POLYTECHNIC UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL TECHNIQUES - POLYNOMIALS;

ELEMENTARY POLYNOMIAL MATRICES; PROJECTIVE MODULES; QUILLEN-SUSLIN THEOREM PROOF; SERRE'S CONJECTURE;

ELECTRONIC CIRCUITS;

EID: 0021442133     PISSN: 00984094     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCS.1984.1085545     Document Type: Article

References (13)

1. V. Belevitch, Classical Network Theory. San Francisco, CA: Holden-Day, 1968.
2. R. Newcomb, Linear Multiport Synthesis. New York: McGraw Hill, 1966.
3. T. Kailath, Linear Systems. Englewood Cliffs, NJ: Prentice-Hall, 1980.
4. Van Der Waerden, Modem Algebra, vol. 2, New York: Ungar, 1950.
5. D. C. Youla and G. Gnavi, “Notes on n-dimensional system theory,” IEEE Trans. Circuits Syst.,vol, CAS-26, Feb. 1979.
6. J. P. Serre, “Modules projectifs et espace filbre a fibre vectorielle,” Sem. Dubreil-Pisot, no. 23, 1957/1958.
7. D. Quillen, “Projective modules over polynomial rings,” Invent. Math. vol. 36, pp. 167-171,1976.
8. C. C. MacDurfee, The Theory of Matrices. New York: Chelsea, 1946.
9. C. S. Seshadri, “Triviality of vector bundles over the affine space AT2,” in Proc. Nat. Acad. Sci., vol. 44, pp. 456-458,1958.
10. A. A. Suslin, “Projective modules over a polynomial ring are free,” Dokl. Adad. Nauk. S.S.S.R. vol. 229 (1976.) pp. 1063–1066, English translation Soviet Math. Dokl. 17 (1976), 1160–1164 (MR 57 no. 9685).
11. T. Y. Lam, Serre’s conjecture, Lecture Notes in Mathematics 635, New York: Springer-Verlag, 1978.
12. O. Zariski and P. Samuel, Commutative Algebra, vol. II, Princeton, NJ: Van Nostrand, 237-247,1960.
13. D. Passman, The Algebraic Structure of Group Rings. New York: Wiley, Thm. 13.4.8,1977.