It is well known that the component of the zero function in C (X) with the m-topology is the
ideal Cψ (X). Given any ideal I⊆ Cψ (X), we are going to define a topology on C (X) namely …

This paper concerns the coincidence of the socle of a semiprimitive ring (or just a reduced
one, in some cases) with the intersection of all essential prime, essential minimal prime, or …

Let I and J be two ideals in a commutative ring R. The ideal I is called J-prime (resp., J-
semiprime) if a, b∈ J (resp., a∈ J) and ab∈ I (resp., a2∈ I) imply a∈ I or b∈ I (resp., a∈ I) …

Let Cc (X) denotes the subalgebra of C (X) consisting of functions with countable image. Let
Ac (X) be a subring of C (X) that contains Cc (X). For ideals in Ac (X), we define two maps …

In this talk first we give a new representation for closed ideals in C (X) and the intersections
of maximal ideals in C∗(X). Next, for a completely regular Hausdorff space X, we construct a …