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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Main Author: George Georgescu
Format: Article
Language:English
Published: Alexandru Ioan Cuza University of Iasi 2024-12-01
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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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.
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publisher Alexandru Ioan Cuza University of Iasi
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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