On the Inverse Syzygy Problem

REFERENCES

• Auslander , M. , Bridger , M. ( 1969 ). Stable Module Theory . Mem. Amer. Math. Soc. 94 , Providence , RI : American Mathematical Society .
   Google Scholar
• Bourbaki , N. ( 1972 ). Commutative Algebra . Paris : Hermann .
   Google Scholar
• Bourbaki , N. ( 1974 ). Algebra I . Paris : Hermann .
   Google Scholar
• Bourlès , H. , Oberst , U. ( 2009 ). Duality for differential-difference systems over Lie groups . To appear in SIAM J. Control Optim.
   Google Scholar
• Brockett , R. , Willems , J. ( 1974 ). Discretized partial differential equations: examples of control systems defined on modules . Automatica 10 : 507 – 515 .
   Web of Science ®Google Scholar
• Bruns , W. , Vetter , U. ( 1988 ). Determinantal Rings . Lecture Notes in Mathematics 1327 , Berlin : Springer-Verlag .
   Google Scholar
• Bueso , J. , Gómez-Torrecillas , J. , Lobillo , F. ( 2001 ). Homological computations in PBW modules . Alg. Represent. Theo. 4 : 201 – 218 .
   Web of Science ®Google Scholar
• Chyzak , F. , Quadrat , A. , Robertz , D. (2005). Effective algorithms for parametrizing linear control systems over Ore algebras. Appl. Alg. Eng. Comm. Comp. 16:319–376.
   Web of Science ®Google Scholar
• Damiano , A. , Struppa , D. , Vajiac , A. , Vajiac , M. ( 2009 ). Hartogs phenomena and antisyzygies for systems of differential equations . J. Geom. Anal. 19 : 288 – 300 .
   Google Scholar
• Goodearl , K. , Warfield , R. , Jr. ( 2004 ). An Introduction to Noncommutative Noetherian Rings . London Mathematical Society Student Texts 61 , , 2nd edn , Cambridge : Cambridge University Press .
   Google Scholar
• Lam , T. ( 1999 ). Lectures on Modules and Rings . Graduate Texts in Mathematics 189 , New York : Springer-Verlag .
   Google Scholar
• Lam , T. ( 2000 ). On the equality of row rank and column rank . Expos. Math. 18 : 161 – 163 .
   Google Scholar
• Moreno-Frías , M. ( 2003 ). Ext groups of Janet systems . J. Pure Appl. Alg. 182 : 269 – 286 .
   Google Scholar
• Oberst , U. ( 1990 ). Multidimensional constant linear systems . Acta Appl. Math. 20 : 1 – 175 .
   Web of Science ®Google Scholar
• Pommaret , J. ( 1994 ). Partial Differential Equations and Group Theory . Dordrecht : Kluwer .
   Google Scholar
• Pommaret , J. ( 2001 ). Partial Differential Control Theory . Mathematics and Its Applications 530 , Dordrecht : Kluwer .
   Google Scholar
• Quadrat , A. ( 2003 ). The fractional representation approach to synthesis problems: an algebraic analysis viewpoint, Parts I and II . SIAM J. Control Optim. 42 : 266 – 299 and 300–320 .
   Web of Science ®Google Scholar
• Shankar , S. ( 2002 ). The evolution of the concept of controllability . Math. Comp. Modell. Dyn. Sys. 8 : 397 – 406 .
   Web of Science ®Google Scholar
• Zerz , E. ( 2001 ). Extension modules in behavioral linear systems theory . Multidim. Syst. Signal Proc. 12 : 309 – 327 .
   Web of Science ®Google Scholar
• Zerz , E. ( 2007 ). Discrete multidimensional systems over ℤ/nℤ . Sys. Contr. Lett. 56 : 702 – 708 .
   Google Scholar
• Communicated by M. Cohen.
   Google Scholar