On the ideal structure of

Author:
William E. Dietrich

Journal:
Trans. Amer. Math. Soc. **152** (1970), 61-77

MSC:
Primary 46.55

MathSciNet review:
0265941

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Abstract: The ideal structure of , the algebra of continuous functions from a completely regular Hausdorff space to the scalars is analyzed by examining for fixed (the Stone-Čech compactification of ) the structure of the quotient , where is the ideal of maps for which

**[1]**Richard F. Arens,*A topology for spaces of transformations*, Ann. of Math. (2)**47**(1946), 480–495. MR**0017525****[2]**William E. Dietrich Jr.,*A note on the ideal structure of 𝐶(𝑋)*, Proc. Amer. Math. Soc.**23**(1969), 174–178. MR**0268678**, 10.1090/S0002-9939-1969-0268678-6**[3]**William E. Dietrich Jr.,*The maximal ideal space of the topological algebra 𝐶(𝑋,𝐸)*, Math. Ann.**183**(1969), 201–212. MR**0254605****[4]**Leonard Gillman,*Countably generated ideals in rings of continuous functions*, Proc. Amer. Math. Soc.**11**(1960), 660–666. MR**0156189**, 10.1090/S0002-9939-1960-0156189-X**[5]**Leonard Gillman and Meyer Jerison,*Rings of continuous functions*, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR**0116199****[6]**J. Keesling and P. Nanzetta,*On certain ideals of*, Notices Amer. Math. Soc.**16**(1969), 837. Abstract #69T-B165.**[7]**Carl W. Kohls,*Prime ideals in rings of continuous functions*, Illinois J. Math.**2**(1958), 505–536. MR**0102732****[8]**Carl W. Kohls,*Prime ideals in rings of continuous functions. II*, Duke Math. J.**25**(1958), 447–458. MR**0102733****[9]**Saunders Mac Lane,*Homology*, Die Grundlehren der mathematischen Wissenschaften, Bd. 114, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963. MR**0156879****[10]**Neal H. McCoy,*The theory of rings*, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1964. MR**0188241****[11]**Ernest A. Michael,*Locally multiplicatively-convex topological algebras*, Mem. Amer. Math. Soc.,**No. 11**(1952), 79. MR**0051444****[12]**Walter Rudin,*Fourier analysis on groups*, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley and Sons), New York-London, 1962. MR**0152834**

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1970-0265941-2

Keywords:
Completely regular space,
algebra of continuous functions,
Stone-Čech compactification,
prime ideal,
-ideal,
maximal ideal,
minimal ideal,
Krull dimension,
maximal algebra,
minimal algebra

Article copyright:
© Copyright 1970
American Mathematical Society