Abstract
The primary spectrum and the automorphism group of the Jordan plane over a field of nonzero characteristic are described. The problem of extending a prime ideal of the center of the Jordan plane to a primary ideal of the entire algebra is considered.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. N. Shirikov, “Two-generated graded algebras,” Algebra Discrete Math., No. 3, 64–80 (2005).
J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings. With the cooperation of L. W. Small (Wiley, Chichester, 1987).
O. Ore, “Theory of non-commutative polynomials,” Ann. Math. (2) 34 (3), 480–508 (1933).
K. A. Brown and K. R. Goodearl, Lectures on Algebraic Quantum Groups (Birkhäuser, Basel, 2002).
V. A. Artamonov, “Quantum problem Serre,” Uspekhi Mat. Nauk 53 (4), 3–76 (1998) [Math. Surveys 53 (4), 657–730(1998)].
V. A. Artamonov, “Automorphisms and derivations of quantum polynomials,” in Recent Advances in Lie Theory. Selected Contributions to the 1st Colloquium on Lie Theory and Applications, Vigo, Spain, 2000 (Heldermann, Lemgo, 2002), pp. 109–120 (2002).
V. A. Artamonov, “Action of Hopf algebras on generic quantum Mal’tsev power series and quantum planes,” Sovrem.Mat. Prilozh. 18, Algebra, 3–25 (2004) [J. Math. Sci.(N. Y.) 134(1), 1773–1798(2006)].
V. A. Jategaonkar, “A multiplicative analog of the Weyl algebra,” Comm. Algebra 12 (13–14), 1669–1688 (1984).
I. N. Herstein, Noncommutative Rings (Wiley, New York, 1968; Mir, Moscow, 1972).
E. B. Vinberg, A Course in Algebra (Factorial Press, Moscow, 2001; Amer. Math. Soc, Providence, RI, 2003).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Shirikov, E.N. The Jordan plane over a field of positive characteristic. Math Notes 82, 238–256 (2007). https://doi.org/10.1134/S0001434607070292
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1134/S0001434607070292