Maximal ideals in subalgebras of
Lothar Redlin and Saleem Watson
Proc. Amer. Math. Soc. 100 (1987), 763-766
Primary 54C40; Secondary 46E25, 46J20
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Abstract: Let be a completely regular space, and let be a subalgebra of containing . We study the maximal ideals in by associating a filter to each . This association extends to a one-to-one correspondence between (the set of maximal ideals of ) and . We use the filters to characterize the maximal ideals and to describe the intersection of the free maximal ideals in . Finally, we outline some of the applications of our results to compactifications between and .
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