z-Ideals and zº-Ideals in the Factor Rings of C(X)
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On $z$-ideals of pointfree function rings
Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of continuous real-valued functions on $L$. We show that the lattice $Zid(mathcal{R}L)$ of $z$-ideals of $mathcal{R}L$ is a normal coherent Yosida frame, which extends the corresponding $C(X)$ result of Mart'{i}nez and Zenk. This we do by exhibiting $Zid(mathcal{R}L)$ as a quotient of $Rad(mathcal{R}L)$, the ...
full textz-weak ideals and prime weak ideals
In this paper, we study a generalization of z-ideals in the ring C(X) of continuous real valued functions on a completely regular Hausdorff space X. The notion of a weak ideal and naturally a weak z-ideal and a prime weak ideal are introduced and it turns out that they behave such as z-ideals in C(X).
full texton $z$-ideals of pointfree function rings
let $l$ be a completely regular frame and $mathcal{r}l$ be the ring of continuous real-valued functions on $l$. we show that the lattice $zid(mathcal{r}l)$ of $z$-ideals of $mathcal{r}l$ is a normal coherent yosida frame, which extends the corresponding $c(x)$ result of mart'{i}nez and zenk. this we do by exhibiting $zid(mathcal{r}l)$ as a quotient of $rad(mathcal{r}l)$, the ...
full textz_R-Ideals and z^0_R -Ideals in Subrings of R^X
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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Journal title
volume 36 issue No. 1
pages 211- 226
publication date 2011-01-23
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