Journal of Applied Mathematics and Computation

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Article http://dx.doi.org/10.26855/jamc.2023.03.010

M-ideals of a Uniquely Representable De Morgan Quasiring

Huaxin Mei*, Congwen Luo

Department of Mathematics and Three Gorges Mathematics Research Center, China Three Gorges University, Yichang, Hubei, China.

*Corresponding author: Huaxin Mei

Published: April 14,2023

Abstract

The concept of a (Boolean) quasiring was introduced by Dorninger, Langer and  Maczynski in order to get a ring-like counterpart of an orthomodular lattice. Various types of such quasirings were described and compared by the authors in “A note on orthopseudorings and Boolean quasirings”. A similar way was applied when ring-like structures were assigned to De Morgan algebras in Chajda I, Eigenthaler G. (2008). The resulting ring-like structures were called De Morgan quasirings. De Morgan quasirings are used as algebraic models in the foundations of Lukasiewicz logic, constructive logic with strong negation. Chajda and Eigenthaler established a common axiom system for both De Morgan quasirings and De Morgan algebras and showed how an interval of a De Morgan algebra (or De Morgan quasiring) can be viewed as a De Morgan algebra (or De Morgan quasiring, respectively). In this paper, we give a characterization of the M-ideals within a uniquely representable De Morgan quasiring  R and show that all the M-ideals of form a distributive lattice under set inclusion.

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How to cite this paper

M-ideals of a Uniquely Representable De Morgan Quasiring

How to cite this paper:  Huaxin Mei, Congwen Luo. (2023) M-ideals of a Uniquely Representable De Morgan QuasiringJournal of Applied Mathematics and Computation7(1), 101-107.

DOI: http://dx.doi.org/10.26855/jamc.2023.03.010