| Title:
|
An interesting class of ideals in subalgebras of $C(X)$ containing $C^*(X)$ (English) |
| Author:
|
Acharyya, Sudip Kumar |
| Author:
|
De, Dibyendu |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
48 |
| Issue:
|
2 |
| Year:
|
2007 |
| Pages:
|
273-280 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the present paper we give a duality between a special type of ideals of subalgebras of $C(X)$ containing $C^*(X)$ and $z$-filters of $\beta X$ by generalization of the notion $z$-ideal of $C(X)$. We also use it to establish some intersecting properties of prime ideals lying between $C^*(X)$ and $C(X)$. For instance we may mention that such an ideal becomes prime if and only if it contains a prime ideal. Another interesting one is that for such an ideal the residue class ring is totally ordered if and only if it is prime. (English) |
| Keyword:
|
Stone-Čech compactification |
| Keyword:
|
rings of continuous functions |
| Keyword:
|
maximal ideals |
| Keyword:
|
$z^{\beta}_A$-ideals |
| MSC:
|
54C30 |
| MSC:
|
54C35 |
| MSC:
|
54C40 |
| MSC:
|
54D35 |
| idZBL:
|
Zbl 1199.54153 |
| idMR:
|
MR2338095 |
| . |
| Date available:
|
2009-05-05T17:02:51Z |
| Last updated:
|
2012-05-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119657 |
| . |
| Reference:
|
[1] Acharyya S.K., Chattopadhyay K.C., Ghosh D.P.: A class of subalgebras of $ C(X)$ and the associated compactness.Kyungpook Math. J. 41 2 (2001), 323-324. Zbl 1012.54024, MR 1876202 |
| Reference:
|
[2] Byun H.L., Watson S.: Prime and maximal ideals of $ C(X)$.Topology Appl. 40 (1991), 45-62. MR 1114090 |
| Reference:
|
[3] De D., Acharyya S.K.: Characterization of function rings between $C^*(X)$ and $C(X)$.Kyungpook Math. J. 46 (2006), 503-507. Zbl 1120.54014, MR 2282652 |
| Reference:
|
[4] Dominguege J.M., Gomez J., Mulero M.A.: Intermediate algebras between $C^{*}(X)$ and $C(X)$ as rings of fractions of $ C^*(X)$.Topology Appl. 77 (1997), 115-130. MR 1451646 |
| Reference:
|
[5] Gillman L., Jerison M.: Rings of Continuous Functions.Springer, New York, 1976. Zbl 0327.46040, MR 0407579 |
| Reference:
|
[6] Henriksen M., Johnson D.G.: On the structure of a class of archimedean lattice ordered algebras.Fund. Math. 50 (1961), 73-94. Zbl 0099.10101, MR 0133698 |
| Reference:
|
[7] Plank D.: On a class of subalgebras of $ C(X)$ with application to $\beta X-X$.Fund. Math. 64 (1969), 41-54. MR 0244953 |
| Reference:
|
[8] Redlin L., Watson S.: Maximal ideals in subalgebras of $ C(X)$.Proc. Amer. Math. Soc. 100 (1987), 763-766. Zbl 0622.54011, MR 0894451 |
| . |
