Mathematics

Researchers from Saginaw Valley State University discuss findings in algebra

  2008 NOV 24 - (VerticalNews.com) -- "Let k be an algebraically closed field of arbitrary characteristic," investigators in the United States report.

  "We give a self-contained algebraic proof of the following statement: If V is an affine surface over k such that V x k congruent to k(3), then V congruent to k(2). This fact, which is due to Fujita, Miyanishi, Sugie, and Russell, solves the Zariski cancellation problem for surfaces," wrote A.J. Crachiola and colleagues, Saginaw Valley State University.

  The researchers concluded: "To achieve our proof, we first show that if A is a finitely generated domain with AK(A) = A, then AK(A[x]) = A."

  Crachiola and colleagues published their study in the Journal of Algebra (An algebraic proof of a cancellation theorem for surfaces. Journal of Algebra, 2008;320(8):3113-3119).

  For additional information, contact A.J. Crachiola, Saginaw Valley State University, Dept. of Math Science, 7400 Bay Rd., University Center, MI 48710, USA.

  The publisher of the Journal of Algebra can be contacted at: Academic Press Inc. Elsevier Science, 525 B St., Ste. 1900, San Diego, CA 92101-4495, USA.

  Keywords: Algebra, Mathematics, Saginaw Valley State University.

  This article was prepared by VerticalNews Mathematics editors from staff and other reports. Copyright 2008, VerticalNews Mathematics via VerticalNews.com.