247
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

A Class of Simple Derivations of k[x, y]

Pages 4066-4083 | Received 01 Aug 2012, Published online: 23 Apr 2014

REFERENCES

  • Coutinho , S. C. ( 2007 ). Nonholonomic simple D-modules from simple derivations . Glasg. Math. J. 49 : 11 – 21 .
  • de Souza Doering , A. M. , Lequain , Y. , Ripoll , C. ( 2006 ). Differential simplicity and cyclic maximal ideals of the Weyl algebra A 2(K) . Glasg. Math. J. 48 : 269 – 274 .
  • Goodearl , K. R. , Warfield Jr. , R. B. ( 1989 ). An introduction to noncommutative Noetherian rings. London Mathematical Society Student Texts 16. Cambridge: Cambridge University Press .
  • Gavran , V. S. ( 2009 ). Simple derivations of higher degree in two variables . Ukraïn. Mat. Zh. 61 : 568 – 571 .
  • Jordan , D. A. ( 1981 ). Differentially simple ring with no invertible derivatives . Quart J. Math. Oxford Ser. ( 2 ) 32 : 417 – 424 .
  • Kaplansky , I. ( 1976 ). An Introduction to Differetial Algebra. Hermann, Paris .
  • Kour , S. ( 2012 ). Some simple derivations of k[x, y] . Comm. Algebra 40 : 4100 – 4110 .
  • Kour , S. , Maloo , A. K. ( 2013 ). Simplicity of Some derivations of k[x, y] . Comm. Algebra 41 : 1417 – 1431 .
  • Lequain , Y. ( 1971 ). Differential simplicity and complete integral closure . Pacific Journal of Math. 36 : 741 – 751 .
  • Lequain , Y. ( 2008 ). Simple Shamsuddin derivations of K[X, Y 1, ⋅, Y n ]: An algorithmic characterization . J. Pure Appl. Algebra 212 : 801 – 807 .
  • Lequain , Y. , Levcovitz , D. , de Souza Junior , J. C. ( 2005 ). D-simple rings and principal maximal ideals of the Weyl algebra . Glasg. Math. J. 47 : 269 – 285 .
  • Maciejewski , A. , Moulin Ollagnier , J. , Nowicki , A. ( 2001 ). Simple quadratic derivations in two variables . Comm. Algebra 29 : 5095 – 5113 .
  • Matsumura , H. ( 1989 ). Commutative Ring Theory . Cambridge : Cambridge University Press .
  • Nowicki , A. ( 1994 ). Polynomial Derivations and their Rings of Constants. Uniwersytet Mikolaja Kopernika, Toruń .
  • Nowicki , A. ( 2008 ). An example of a simple derivation in two variables . Colloq. Math. 113 : 25 – 31 .
  • Moulin Ollagnier , J. , Nowicki , A. ( 2008 ). Derivations of polynomial algebra without Darboux polynomials . J. Pure Appl. Algebra 212 : 1626 – 1631 .
  • Communicated by M. Bresar.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.