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Original Articles

Test Sets and Test Rank of a Free Metabelian Lie Algebra

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Pages 5581-5589 | Received 01 Jun 2002, Published online: 31 Aug 2006

References

  • Bahturin , Yu. A. , Mikhalev , A. A. , Zaicev , M. V. and Petrogradsky , V. M. 1992 . Infinite Dimensional Lie Superalgebras Berlin-New York : Walter de Grayter Publications .
  • Bokut , L. A. and Kukin , G. P. 1994 . Algorithmic and Combinatorial Algebra Dordrecht : Kluwer Academic Publications .
  • Chirkov , I. V. and Shevelin , M. A. 2000 . Determination of endomorphisms of free metabelian Lie algebras . Siberian Math. J. , 6 ( 41 ) : 1457 – 1460 .
  • Drensky , V. and Yu , J. T. 1998 . Orbits in free algebras of rank two . Commun. Algebra , 26 ( 6 ) : 1895 – 1906 .
  • Fox , R. H. 1995 . Free differential calculus. I. Derivations in free group rings . Ann. Math. , 2 ( 57 ) : 547 – 560 .
  • Mikhalev , A. A. and Zolotykh , A. A. 1995 . Combinatorial Aspects of Lie Superalgebras New York, Boca Raton : CRC Press .
  • Mikhalev , A. A. and Yu , J. T. 2000 . Primitive, almost primitive, test, and Δ-primitive elements of free algebras with the Nielsen-Schreier property . J. Algebra , 228 : 603 – 623 .
  • Reutenauer , C. 1992 . Applications of a noncommutative jacobian matrix . J. Pure Appl. Algebra , 77 : 169 – 181 .
  • Reutenauer , C. 1993 . Free Lie Algebras Oxford : Clarendon Press .
  • Shmelkin , A. L. 1966 . Free polynilpotent groups . Izv. Acad. Nauk SSSR Ser. Math. Soc. Transl. Ser. 2 , 55 : 270 – 304 . (Providence, RI)
  • Timoshenko , E. I. 1997 . On the definability of endomorphisms of a free group of the variety UM by a finite set of values . Math. Notes , 62 ( 6 ) : 767 – 770 .
  • Timoshenko , E. I. 2000 . Test elements and test rank of a free metabelian group . Siberian Math.J. , 41 ( 6 ) : 1451 – 1456 .
  • Umirbaev, U. U. (1990). Abstract of Reports, On Jacobian Matrices of Lie algebras. In: The VI All-Union School on Varieties of Alg. Systems Magnitogorsk, 32–33

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