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Basic semirings

In: Mathematica Slovaca, vol. 69, no. 3
Ivan Chajda - Helmut Länger

Details:

Year, pages: 2019, 533 - 540
Keywords:
basic algebra, commutative basic algebra, semiring, involution, basic semiring, ideal, congruence
About article:
Basic algebras were introduced by Chajda, Hala\v s and K\"uhr as a common generalization of MV-algebras and orthomodular lattices, i.e.\ algebras used for formalization of non-classical logics, in particular the logic of quantum mechanics. These algebras were represented by means of lattices with section involutions. On the other hand, classical logic was formalized by means of Boolean algebras which can be converted into Boolean rings. A natural question arises if a similar representation exists also for basic algebras. Several attempts were already realized by the authors, see the references. Now we show that if a basic algebra is commutative then there exists a representation via certain semirings with involution similarly as it was done for MV-algebras by Belluce, Di Nola and Ferraioli. These so-called basic semirings, their ideals and congruences are studied in the paper.
How to cite:
ISO 690:
Chajda, I., Länger, H. 2019. Basic semirings. In Mathematica Slovaca, vol. 69, no.3, pp. 533-540. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0245

APA:
Chajda, I., Länger, H. (2019). Basic semirings. Mathematica Slovaca, 69(3), 533-540. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0245
About edition:
Published: 21. 5. 2019