Intermediate algebras in Archimedean semiprime f-algebras
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910808659722240 |
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| author | Boulabiar, Karim |
| author_facet | Boulabiar, Karim |
| contents | We introduce the notion of bounded quasi-inversion closed semiprime f-algebras and we prove that, if A is such an algebra, then any intermediate algebra in A is an order ideal of A. This extends a recent result by Dominguez who has dealt with the unital case (the problem on C(X)-type spaces has been solved earlier by Dominguez, Gomez-Perez, and Mulero). Our results are illustrated by examples of algebras of continuous functions and algebras of measurable functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00600 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intermediate algebras in Archimedean semiprime f-algebras Boulabiar, Karim Functional Analysis We introduce the notion of bounded quasi-inversion closed semiprime f-algebras and we prove that, if A is such an algebra, then any intermediate algebra in A is an order ideal of A. This extends a recent result by Dominguez who has dealt with the unital case (the problem on C(X)-type spaces has been solved earlier by Dominguez, Gomez-Perez, and Mulero). Our results are illustrated by examples of algebras of continuous functions and algebras of measurable functions. |
| title | Intermediate algebras in Archimedean semiprime f-algebras |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2502.00600 |