Artinian and Noetherian vector lattices
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929527783948288 |
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| author | Kandić, Marko Roelands, Mark Wortel, Marten |
| author_facet | Kandić, Marko Roelands, Mark Wortel, Marten |
| contents | In this paper, we study Artinian and Noetherian properties in vector lattices and provide a concrete representation of these spaces. Furthermore, we describe for which Archimedean uniformly complete vector lattices every decreasing sequence of prime ideals is stationary (a property that we refer to as prime Artinian). We also completely characterize the prime ideals in vector lattices of continuous root functions and piecewise polynomials. This is a useful space for studying how having decreasing stationary sequences of prime ideals does not imply having increasing stationary sequences of prime ideals, and vice versa. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_03329 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Artinian and Noetherian vector lattices Kandić, Marko Roelands, Mark Wortel, Marten Functional Analysis 46A40 46B40 In this paper, we study Artinian and Noetherian properties in vector lattices and provide a concrete representation of these spaces. Furthermore, we describe for which Archimedean uniformly complete vector lattices every decreasing sequence of prime ideals is stationary (a property that we refer to as prime Artinian). We also completely characterize the prime ideals in vector lattices of continuous root functions and piecewise polynomials. This is a useful space for studying how having decreasing stationary sequences of prime ideals does not imply having increasing stationary sequences of prime ideals, and vice versa. |
| title | Artinian and Noetherian vector lattices |
| topic | Functional Analysis 46A40 46B40 |
| url | https://arxiv.org/abs/2410.03329 |