Open Access

## K. S. Sabna and N. R. Mangalambal

#### Full Text

In the background of pointfree topology, given a frame $L$ and a frame homomorphism $f: L\longrightarrow L$, for each $b\in L$, ideals of the form $\langle f\rangle_{b}=\{a \in L : \Sigma_{f(a)}\subseteq \Sigma_{b}\}$ is constructed and its properties are studied. These ideals are utilized to form a frame congruence on $L$ and hence a sublocale of $L$. By assigning the proper order, the set $J_{f}=\{\langle f\rangle_{b}: b \in L\}$ has been shaped as a locale of ideals of $L$. An equivalent condition for the locale $J_{f}$ to be compact is also derived.

Keywords:
locale, Ideal, Boolean locale, compact locale, congruence.