Affiliation:
1. Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Abstract
A subalgebra A(X) of C(X) is said to be a ?-subalgebra if it is closed under
bounded inversion and the space of its maximal ideals equipped with the
hull-kernel topology is homeomorphic to ?X with a homeomorphism which leaves
X pointwise fixed. Kharbhih and Dutta in [Closure formula for ideals in
intermediate rings, Appl. Gen. Topol. 21 (2) (2020), 195-200] showed that
the closure of every ideal I of an intermediate ring with the m-topology,
briefly, the m-closure of I, equals the intersection of all maximal ideals
in A(X) containing I. In this paper, we extend this fact to the class of
?-subalgebras which is shown to be a larger class than intermediate rings.
We also study a more extended class of subrings than ?-subalgebras, namely,
LBI-subalgebras, and characterize the conditions under which an
LBI-subalgebra is a ?-subalgebra. Moreover, some known facts in the context
of C(X) and intermediate rings of C(X) are generalized to ?-subalgebras.
Publisher
National Library of Serbia
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1. On m-Closure of Ideals in LBI-Subalgebras;Bulletin of the Iranian Mathematical Society;2024-07-11