@article{Bag_Acharyya_Mandal_2019, title={A class of ideals in intermediate rings of continuous functions}, volume={20}, url={https://polipapers.upv.es/index.php/AGT/article/view/10171}, DOI={10.4995/agt.2019.10171}, abstractNote={<p>For any completely regular Hausdorff topological space X, an intermediate ring A(X) of continuous functions stands for any ring lying between C<sup>âˆ—</sup>(X) and C(X). It is a rather recently established fact that if A(X) â‰ C(X), then there exist non maximal prime ideals in A(X).We offer an alternative proof of it on using the notion of zâ—¦-ideals. It is realized that a P-space X is discrete if and only if C(X) is identical to the ring of real valued measurable functions defined on the σ-algebra β(X) of all Borel sets in X. Interrelation between z-ideals, zâ—¦-ideal and Ʒ<sub>A</sub>-ideals in A(X) are examined. It is proved that within the family of almost P-spaces X, each Ʒ<sub>A</sub> -ideal in A(X) is a zâ—¦-ideal if and only if each z-ideal in A(X) is a zâ—¦-ideal if and only if A(X) = C(X).</p>}, number={1}, journal={Applied General Topology}, author={Bag, Sagarmoy and Acharyya, Sudip Kumar and Mandal, Dhananjoy}, year={2019}, month={Apr.}, pages={109–117} }