For a nonempty topological space $ X $, the ring of all real-valued functions on $ X $ with
pointwise addition and multiplication is denoted by $ F (X) $ and contonuous members of …

For any completely regular Hausdorff topological space X, an intermediate ring A (X) of
continuous functions stands for any ring lying between C ∗(X) and C (X). It is a rather …

Two new topologies are defined on C (X). These topologies make C (X) to be a zero-
dimensional (completely regular) Hausdorff space. C (X) endowed by these topologies is …

Let C (X) be the ring of continuous real-valued functions on a (completely regular)
topological space X. The structure of the prime ideals and the prime z-ideals of C (X) has …

Let X be a nonempty topological space, C (X) F be the set of all real-valued functions on X
which are discontinuous at most on a finite set and B1 (X) be the ring of all real-valued Baire …

Let X be a nonempty topological space, C (X) F be the set of all real-valued functions on X
which are discontinuous at most on a finite set and B1 (X) be the ring of all real-valued Baire …

We have characterized the spaces X for which the smallest z-ideal containing C∞(X) is
prime. It turns out that C∞(X) is a z-ideal in C (X) if and only if every zero-set contained in an …

For a topological space X, let Σ (X) be the family of all subrings of C (X) containing C⁎(X). In
1997, SK Acharyya, KC Chattopadhyay and DP Ghosh showed that for an A (X)∈ Σ (X), the …

For a nonempty topological space X, the ring of all real-valued functions on $ X $ with
pointwise addition and multiplication is denoted by $ F (X) $ and continuous members of $ F …

Let R be a commutative ring with nonzero identity. In this paper, we introduce and
investigate a generalization of (m, n)-closed ideals. Let φ: I (R)→ I (R)∪{∅} be a function …