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Projective Lines Over One-Dimensional Semilocal Domains and Spectra of Birational Extensions

In: Algebraic Geometry and its Applications

Author

Listed:
  • William Heinzer
  • David Lantz
  • Sylvia Wiegand

Abstract

In [7], Nashier asked if the condition on a one-dimensional local domain R that each maximal ideal of the Laurent polynomial ring R[y, y -1] contracts to a maximal ideal in R[y] or in R[y -1] implies that R is Henselian. Motivated by this question, we consider the structure of the projective line Proj(R[s, t]) over a one-dimensional semilocal domain R (the projective line regarded as a topological space, or equivalently as a partially ordered set). In particular, we give an affirmative answer to Nashier’s question. (Nashier has also independently answered his question [9].) Nashier has also studied implications on the prime spectrum of the Henselian property in [8] as well as in the papers cited above.

Suggested Citation

  • William Heinzer & David Lantz & Sylvia Wiegand, 1994. "Projective Lines Over One-Dimensional Semilocal Domains and Spectra of Birational Extensions," Springer Books, in: Chandrajit L. Bajaj (ed.), Algebraic Geometry and its Applications, chapter 19, pages 309-325, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2628-4_19
    DOI: 10.1007/978-1-4612-2628-4_19
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