On a characterization of the maximal ideal spaces of algebraically closed commutative algebras
Authors:
Takeshi Miura and Kazuki Niijima
Journal:
Proc. Amer. Math. Soc. 131 (2003), 28692876
MSC (2000):
Primary 46J10
Published electronically:
December 30, 2002
MathSciNet review:
1974344
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Abstract: Let be the algebra of all complexvalued continuous functions on a compact Hausdorff space . We say that is algebraically closed if each monic polynomial equation over has a continuous solution. We give a necessary and sufficient condition for to be algebraically closed for a locally connected compact Hausdorff space . In this case, it is proved that is algebraically closed if each element of is the square of another. We also give a characterization of a firstcountable compact Hausdorff space such that is algebraically closed.
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Additional Information
Takeshi Miura
Affiliation:
Department of Basic Technology, Applied Mathematics and Physics, Yamagata University, Yonezawa 9928510, Japan
Email:
miura@yz.yamagatau.ac.jp
Kazuki Niijima
Affiliation:
Gumma Prefectural Ôta Technical High School, 380 Motegichou, Ôta 3730809, Japan
DOI:
http://dx.doi.org/10.1090/S0002993902068351
PII:
S 00029939(02)068351
Keywords:
Commutative Banach algebras,
maximal ideal spaces
Received by editor(s):
April 24, 2001
Received by editor(s) in revised form:
April 10, 2002
Published electronically:
December 30, 2002
Communicated by:
N. TomczakJaegermann
Article copyright:
© Copyright 2002
American Mathematical Society
