منابع مشابه
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 ...
متن کاملon $z$-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 ...
متن کاملA note on lattices of z-ideals of f-rings
The lattice of z-ideals of the ring C(X) of real-valued continuous functions on a completely regular Hausdorff space X has been shown by Mart́ınez and Zenk to be a complete Heyting algebra with certain properties. We show that these properties are due only to the fact that C(X) is an f -ring with bounded inversion. This we do by studying lattices of algebraic z-ideals of abstract f -rings with b...
متن کاملOn lattice of basic z-ideals
For an f-ring with bounded inversion property, we show that , the set of all basic z-ideals of , partially ordered by inclusion is a bounded distributive lattice. Also, whenever is a semiprimitive ring, , the set of all basic -ideals of , partially ordered by inclusion is a bounded distributive lattice. Next, for an f-ring with bounded inversion property, we prove that is a complemented...
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ژورنال
عنوان ژورنال: Mathematica Slovaca
سال: 2018
ISSN: 1337-2211,0139-9918
DOI: 10.1515/ms-2017-0099