Prime ideals in rings of continuous functions
نویسندگان
چکیده
منابع مشابه
Localization at prime ideals in bounded rings
In this paper we investigate the sufficiency criteria which guarantee the classical localization of a bounded ring at its prime ideals.
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In a commutative Noetherian local complex normed algebra which is complete in its M-adic metric there are only finitely many closed prime ideals.
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A ring of continuous functions is a ring of the form C(X), the ring of all continuous real-valued functions on a completely regular Hausdorff space X. With each ideal / of C(X), we associate certain subalgebras of C(X), and discuss their structure spaces. We give necessary and sufficient conditions for two ideals in rings of continuous functions to have homeomorphic structure spaces. Introducti...
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1. Results. Scattered results about countably2 generated ideals in C(X) are established in [2] and [4] : Op is countably generated if and only if pEX and p has a countable base of neighborhoods; Op is both prime and countably generated if and only if Mp is principal, and if and only if pEX and p is isolated; no lower prime ideal is countably generated. We generalize these as follows: if Mp is c...
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The ideal I 1 generated by the 2 2 quantum minors in the coordinate algebra of quantum matrices, O q (M m;n (k)), is investigated. Analogues of the First and Second Fundamental Theorems of Invariant Theory are proved. In particular, it is shown that I 1 is a completely prime ideal, that is, O q (M m;n (k))=I 1 is an integral domain, and that O q (M m;n (k))=I 1 is the ring of coinvariants of a ...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1958
ISSN: 0019-2082
DOI: 10.1215/ijm/1255454113