Affine and projective lines

over one-dimensional semilocal domains

Author:
Chandni Shah

Journal:
Proc. Amer. Math. Soc. **124** (1996), 697-705

MSC (1991):
Primary 13A17, 13B25, 13E05, 13H99, 13J15

DOI:
https://doi.org/10.1090/S0002-9939-96-03159-0

MathSciNet review:
1301048

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We characterize those partially ordered sets that can occur as the spectra of polynomial rings over one-dimensional semilocal (Noetherian) domains. We also determine the posets that can occur as projective lines over one-dimensional semilocal domains.

**[HLW]**W. Heinzer, D. Lantz, and S. Wiegand,*Projective lines over one-dimensional semilocal domains and spectra of birational extensions*, Proceedings of Conference on Algebraic Geometry and Its Applications, Springer, New York, 1994, pp. (309--325). CMP**94:11****[HW]**W. Heinzer and S. Wiegand,*Prime ideals in two-dimensional polynomial rings*, Proc. Amer. Math. Soc.**107**(1989), 577--586. MR**90b:13010****[HM]**R. Heitmann and S. McAdam,*Comaximizable primes*, Proc. Amer. Math. Soc.**112**(1989), 661--669. MR**91j:13005****[K]**I. Kaplansky,*Commutative rings*, The University of Chicago Press, Chicago, IL, 1974. MR**49:10674****[Ku]**E. Kunz,*Introduction to commutative algebra and algebraic geometry*, Birkhäuser, Boston, MA, 1985. MR**86e:14001****[Ma]**H. Matsumura,*Commutative ring theory*, Cambridge University Press, Cambridge, 1986. MR**88h:13001****[M1]**S. McAdam,*Intersections of height two primes*, J. Algebra**49**(1977), 315--321. MR**58:644****[M2]**------,*Uppers in*, Comm. Algebra**22**(1994), 1349--1362. MR**94j:13007****[MS]**S. McAdam and C. Shah,*Substructures of Spec*, J. Algebra (to appear).**[N]**M. Nagata,*Local Rings*, Interscience, New York, 1962. MR**27:5790****[S]**C. Shah,*Prime ideals lying over zero in polynomial rings*, J. Algebra**175**(1995), 188--198.**[W]**R. Wiegand,*The Prime spectrum of a two-dimensional affine domain*, J. Pure Appl. Algebra**40**(1986), 209--214. MR**87d:14002**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
13A17,
13B25,
13E05,
13H99,
13J15

Retrieve articles in all journals with MSC (1991): 13A17, 13B25, 13E05, 13H99, 13J15

Additional Information

**Chandni Shah**

Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, California 90089-1113

Address at time of publication:
Department of Mathematics, University of California, Riverside, California 92521

Email:
cshah@ucrmath.ucr.edu

DOI:
https://doi.org/10.1090/S0002-9939-96-03159-0

Keywords:
Prime spectrum,
Henselian ring,
polynomial ring,
projective line,
discrete valuation domain

Received by editor(s):
August 30, 1994

Communicated by:
Wolmer V. Vasconcelos

Article copyright:
© Copyright 1996
American Mathematical Society