On the essentiality and primeness of λ-super socle of C(X)
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...
| Published in: | Applied General Topology |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Universitat Politècnica de València
2018-10-01
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| Subjects: | |
| Online Access: | https://polipapers.upv.es/index.php/AGT/article/view/9058 |
| Summary: | 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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| ISSN: | 1576-9402 1989-4147 |