In this article, we investigate new topological descriptions for two well-known mappings and defined on intermediate rings of . Using this, coincidence of each two classes of -ideals, -ideals and -ideals of is studied. Moreover, we answer five questions concerning the mapping raised in [J. Sack, S. Watson, and among intermediate rings, Topology Proc. 43 (2014), 69–82].
Let denote a subalgebra of which is closed under local bounded inversion, briefly, an -subalgebra. These subalgebras were first introduced and studied in Redlin L., Watson S., Structure spaces for rings of continuous functions with applications to realcompactifications, Fund. Math. 152 (1997), 151–163. By characterizing maximal ideals of , we generalize the notion of -ideals, which was first introduced in Acharyya S.K., De D., An interesting class of ideals in subalgebras of containing...
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