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Abstrakty
Let X be a completely regular topological space. Let A(X) be a ring of continuous functions between C(X) and C{X), that is, C*{X) ⊆ A(X) ⊆ C(X). In [9], a correspondence Z_A between ideals of A(X) and z-filters on X is defined. Here we show that Z A extends the well-known correspondence for C* (X) to all rings A(X). We define a new correspondence 3 A and show that it extends the well-known correspondence for C(X) to all rings A{X). We give a formula that relates the two correspondences. We use properties of Z A. and 3 A to characterize C* (X) and C(X) among all rings A(X). We show that 3A defines a one-one correspondence between maximal ideals in A(X) and the z-ultrafilters in X.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Strony
11--20
Opis fizyczny
Bibliogr. 11 poz.
Twórcy
autor
autor
autor
- California State University, Long Beach Department of Mathematics, California State University, Long Beach, Long Beach, CA 90840, joshua.sack@gmail.com
Bibliografia
- [1] W. Adamski; Two ultrafilter properties for vector lattices of real-valued functions, Publ. Math. Debrecen 45 (1994), 225-267.
- [2] H. L. Byun, and S. Watson; Prime and maximal ideals in subrings of C{X), Topology Appl. 40 (1991), 45-62.
- [3] H. L. Byun, and S. Watson; Local bounded inversion in rings of continuous functions, Comment. Math. 37 (1997), 55-63.
- [4] H. L. Byun, L. Redlin, and S. Watson; A-compactifications and rings of continuous functions between C* and C, Topological Vector Spaces, Algebras, and Related Areas, Pitman Research Notes in Mathematics Series 316 (1995), 130-139.
- [5] H. L. Byun, L. Redlin, and S. Watson; Local invertibility in subrings of C* (X)., Bull. Austral. Math. Soc. 46 (1992), no. 3, 449-458.
- [6] L. Gillman and M. Jerison; Rings of Continuous Functions, Springer-Verlag, New York, 1978.
- [7] M. Hendricksen, J. R. Isbell, and D. G. Johnson; Residue class fields of lattice-ordered algebras, Fund. Math. 50 (1961), 107-117.
- [8] D. Plank; On a class of subalgebras of C{X) with applications to (3X - X, Fund. Math. 64 (1969), 41-54.
- [9] L. Redlin and S. Watson; Maximal ideals in subalgebras of C(X), Proc. Amer. Math. Soc. 100 (1987), 763-766.
- [10] L. Redlin and S. Watson; Structure spaces for rings of continuous functions with applications to realcompactifications, Fund. Math. 152 (1997), 151-163.
- [11] S. Willard; General Topology, Addison-Wesley, Reading, MA, 1970.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS8-0023-0059