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.
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References
[1]Shreeram S. Abhyankar, William Heinzer, and Sylvia Wiegand, On the compositum of two power series rings, Proc. Amer. Math. Soc., to appear.
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Roger Wiegand, The prime spectrum of a two-dimensional affine domain,J. Pure Appl. Algebra, 40, 1986, pp. 209–214
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© 1994 Springer-Verlag New York, Inc.
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Heinzer, W., Lantz, D., Wiegand, S. (1994). Projective Lines Over One-Dimensional Semilocal Domains and Spectra of Birational Extensions. In: Bajaj, C.L. (eds) Algebraic Geometry and its Applications. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2628-4_19
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DOI: https://doi.org/10.1007/978-1-4612-2628-4_19
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