SACS | Higher Order mz-elements in Coherent Quantales

Published in Volume XXXIV, Issue 2, 2024, pages 163-187, doi: 10.47743/SACS.2024.2.163

Authors: G. Georgescu

Abstract

The mz-elements of a coherent quantale have recently been de- fined 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 mzⁿ-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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Bibtex

@article{sacscuza:georgescu2024hocq,
  title={Higher Order mz-elements in Coherent Quantales},
  author={G. Georgescu},
  journal={Scientific Annals of Computer Science},
  volume={34},
  number={2},
  organization={Alexandru Ioan Cuza University, Ia\c si, Rom\^ania},
  year={2024},
  pages={163-187},
  publisher={Alexandru Ioan Cuza University Press, Ia\c si},
  doi={10.47743/SACS.2024.2.163}
}