Higher Order mz-elements in Coherent Quantales
The mz-elements of a coherent quantale have recently been defined by the author as an abstraction of the mz-ideals of a unital commutative ring. Having as its starting point the Dube and Ighedo recent paper on higher order ideals in ring theory, this paper deals with the higher order mz-elements...
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| Format: | Article |
| Language: | English |
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Alexandru Ioan Cuza University of Iasi
2024-12-01
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| Series: | Scientific Annals of Computer Science |
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| Online Access: | https://publications.info.uaic.ro/scientific-annals-of-computer-science/sacs-volumes/xxxiv-2/higher-order-mz-elements-in-coherent-quantales/ |
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| _version_ | 1846133875757023232 |
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| author | George Georgescu |
| author_facet | George Georgescu |
| author_sort | George Georgescu |
| collection | DOAJ |
| description | The mz-elements of a coherent quantale have recently been defined by the author as an abstraction of the mz-ideals of a unital commutative ring.
Having as its starting point the Dube and Ighedo recent paper on higher order ideals in ring theory, this paper deals with the higher order mz-elements of a coherent quantale A. For each natural number n we define the mz^n-elements of A, so we obtain an ascending sequence that covers the set of all higher order mz-elements. We obtain a lot of properties of this sequence. In particular, the stationarity of the sequence is studied. Another category of results investigates how the coherent quantale morphisms preserve such properties. |
| format | Article |
| id | doaj-art-c0ea6a9965484c5fa241da45f93cf40f |
| institution | Kabale University |
| issn | 1843-8121 2248-2695 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Alexandru Ioan Cuza University of Iasi |
| record_format | Article |
| series | Scientific Annals of Computer Science |
| spelling | doaj-art-c0ea6a9965484c5fa241da45f93cf40f2024-12-09T13:30:49ZengAlexandru Ioan Cuza University of IasiScientific Annals of Computer Science1843-81212248-26952024-12-01XXXIV216318710.47743/SACS.2024.2.163Higher Order mz-elements in Coherent QuantalesGeorge Georgescu0Faculty of Mathematics and Computer Science, University of Bucharest, Bucharest, RomaniaThe mz-elements of a coherent quantale have recently been defined by the author as an abstraction of the mz-ideals of a unital commutative ring. Having as its starting point the Dube and Ighedo recent paper on higher order ideals in ring theory, this paper deals with the higher order mz-elements of a coherent quantale A. For each natural number n we define the mz^n-elements of A, so we obtain an ascending sequence that covers the set of all higher order mz-elements. We obtain a lot of properties of this sequence. In particular, the stationarity of the sequence is studied. Another category of results investigates how the coherent quantale morphisms preserve such properties.https://publications.info.uaic.ro/scientific-annals-of-computer-science/sacs-volumes/xxxiv-2/higher-order-mz-elements-in-coherent-quantales/coherent quantalesmz-elementsmz^n-elementsmzterminating quantaleradically mz-covered quantale |
| spellingShingle | George Georgescu Higher Order mz-elements in Coherent Quantales Scientific Annals of Computer Science coherent quantales mz-elements mz^n-elements mzterminating quantale radically mz-covered quantale |
| title | Higher Order mz-elements in Coherent Quantales |
| title_full | Higher Order mz-elements in Coherent Quantales |
| title_fullStr | Higher Order mz-elements in Coherent Quantales |
| title_full_unstemmed | Higher Order mz-elements in Coherent Quantales |
| title_short | Higher Order mz-elements in Coherent Quantales |
| title_sort | higher order mz elements in coherent quantales |
| topic | coherent quantales mz-elements mz^n-elements mzterminating quantale radically mz-covered quantale |
| url | https://publications.info.uaic.ro/scientific-annals-of-computer-science/sacs-volumes/xxxiv-2/higher-order-mz-elements-in-coherent-quantales/ |
| work_keys_str_mv | AT georgegeorgescu higherordermzelementsincoherentquantales |