Ideals in $C_B(X)$ arising from ideals in $X$
نویسندگان
چکیده
منابع مشابه
On ideals of ideals in $C(X)$
In this article, we have characterized ideals in $C(X)$ in which every ideal is also an ideal (a $z$-ideal) of $C(X)$. Motivated by this characterization, we observe that $C_infty(X)$ is a regular ring if and only if every open locally compact $sigma$-compact subset of $X$ is finite. Concerning prime ideals, it is shown that the sum of every two prime (semiprime) ideals of e...
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in this article, we have characterized ideals in $c(x)$ in which every ideal is also an ideal (a $z$-ideal) of $c(x)$. motivated by this characterization, we observe that $c_infty(x)$ is a regular ring if and only if every open locally compact $sigma$-compact subset of $x$ is finite. concerning prime ideals, it is shown that the sum of every two prime (semiprime) ideals of e...
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The minimal prime decomposition for semiprime ideals is defined and studied on z-ideals of C(X). The necessary and sufficient condition for existence of the minimal prime decomposition of a z-ideal / is given, when / satisfies one of the following conditions: (i) / is an intersection of maximal ideals. (ii) I is an intersection of O , s, when X is basically disconnected. (iii) I=O , when x X h...
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The free resolution and the Alexander dual of squarefree monomial ideals associated with certain subsets of distributive lattices are studied.
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Let X be a topological space and R be a subring of RX. By determining some special topologies on X associated with the subring R, characterizations of maximal fixxed and maximal growing ideals in R of the form Mx(R) are given. Moreover, the classes of zR-ideals and z0R-ideals are introduced in R which are topological generalizations of z-ideals and z0-ideals of C(X), respectively. Various c...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 2019
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm170807-27-9