On the essentiality and primeness of λ-super socle of C(X)

S. Mehran; M. Namdari; S. Soltanpour

doi:10.4995/agt.2018.9058

Authors

S. Mehran Islamic Azad University
M. Namdari Shahid Chamran University of Ahvaz
S. Soltanpour Petroleum University of Technology

DOI:

https://doi.org/10.4995/agt.2018.9058

Keywords:

λ-super socle of C(X), λ-isolated point, λ-disjoint spaces

Abstract

Spaces X for which the annihilator of Sλ(X), the λ-super socle of C(X) (i.e., the set of elements of C(X) that cardinality of their cozerosets are less than λ, where λ is a regular cardinal number such that λ≤|X|) is generated by an idempotent are characterized. This enables us to find a topological property equivalent to essentiality of Sλ(X). It is proved that every prime ideal in C(X) containing Sλ(X) is essential and it is an intersection of free prime ideals. Primeness of Sλ(X) is characterized via a fixed maximal ideal of C(X).

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Author Biographies

S. Mehran, Islamic Azad University

Shoushtar Branch

Department of Mathematics

M. Namdari, Shahid Chamran University of Ahvaz

Department of Mathematics

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