The space of minimal prime ideals of need not be basically disconnected
Authors:
A. Dow, M. Henriksen, Ralph Kopperman and J. Vermeer
Journal:
Proc. Amer. Math. Soc. 104 (1988), 317320
MSC:
Primary 54C40; Secondary 06F25
MathSciNet review:
958091
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Abstract: Problems posed twenty and twentyfive years ago by M. Henriksen and M. Jerison are solved by showing that the space of minimal prime ideals of the ring of continuous realvalued functions on a compact (Hausdorff) space need not be basically disconnectedor even an space.
 [DHKV]
A. Dow, M. Henriksen, R. Kopperman and J. Vermeer, The countable annihilator condition and weakly Lindelöf subspaces of minimal prime ideals (submitted).
 [GH]
L. Gillman and M. Henriksen, Rings of continuous functions inn which finitely generated ideals are principal, Trans. Amer. Math. Soc. 82 (1956), 366391.
 [GJ]
L. Gillman and M. Jerison, Rings of continuous functions, Van Nostrand, Princeton, N. J., 1960.
 [HJ]
M. Henriksen and M. Jerison, The space of minimal prime ideals of a commutative ring, General Topology and its Relations to Modern Analysis and Algebra (Prague, 1962), and Trans. Amer. Math. Soc. 115 (1965), 110130.
 [Ho]
M. Hochster, Prime ideal structure in commutative rings, Trans. Amer. Math. Soc. 142 (1969), 4360.
 [K]
J. Kist, Minimal prime ideals in commutative semigroups, Proc. London Math. Soc. (3) 13 (1963), 3150.
 [Ku]
K. Kunen, Some points in , Math. Proc. Cambridge Philos. Soc. 80 (1976), 385398.
 [vM]
J. van Mill, An introduction to , Handbook of SetTheoretic Topology, NorthHolland, Amsterdam, 1984.
 [W]
R. Walker, The StoneČech compactification, SpringerVerlag, Berlin and New York, 1974.
 [Wo]
R. G. Woods, A survey of absolutes of topological spaces, Topological Structures II, Mathematical Centre Tracts, no. 116, 1979, pp. 323362.
 [DHKV]
 A. Dow, M. Henriksen, R. Kopperman and J. Vermeer, The countable annihilator condition and weakly Lindelöf subspaces of minimal prime ideals (submitted).
 [GH]
 L. Gillman and M. Henriksen, Rings of continuous functions inn which finitely generated ideals are principal, Trans. Amer. Math. Soc. 82 (1956), 366391.
 [GJ]
 L. Gillman and M. Jerison, Rings of continuous functions, Van Nostrand, Princeton, N. J., 1960.
 [HJ]
 M. Henriksen and M. Jerison, The space of minimal prime ideals of a commutative ring, General Topology and its Relations to Modern Analysis and Algebra (Prague, 1962), and Trans. Amer. Math. Soc. 115 (1965), 110130.
 [Ho]
 M. Hochster, Prime ideal structure in commutative rings, Trans. Amer. Math. Soc. 142 (1969), 4360.
 [K]
 J. Kist, Minimal prime ideals in commutative semigroups, Proc. London Math. Soc. (3) 13 (1963), 3150.
 [Ku]
 K. Kunen, Some points in , Math. Proc. Cambridge Philos. Soc. 80 (1976), 385398.
 [vM]
 J. van Mill, An introduction to , Handbook of SetTheoretic Topology, NorthHolland, Amsterdam, 1984.
 [W]
 R. Walker, The StoneČech compactification, SpringerVerlag, Berlin and New York, 1974.
 [Wo]
 R. G. Woods, A survey of absolutes of topological spaces, Topological Structures II, Mathematical Centre Tracts, no. 116, 1979, pp. 323362.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002993919880958091X
PII:
S 00029939(1988)0958091X
Article copyright:
© Copyright 1988 American Mathematical Society
