Localization of PMV-algebras

Localization of PMV-algebras

In this paper, we show that the going up and lying over theorems hold in PMV -algebras, and we prove that every · -prime ideal in a PMV -subalgebra is the intersection of a · -prime ideal in the overalgebra with the subalgebra. Also, we show that if P is a · -prime ideal of a unital PMV -algebra A a...

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Veröffentlicht in:Soft computing (Berlin, Germany) Germany), 2018-01, Vol.22 (1), p.31-40
Hauptverfasser: Banivaheb, H., Saeid, A. Borumand
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Artificial Intelligence
Computational Intelligence
Control
Engineering
Foundations
Intersections
Localization
Mathematical Logic and Foundations
Mechatronics
Robotics
Theorems
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Zusammenfassung:In this paper, we show that the going up and lying over theorems hold in PMV -algebras, and we prove that every · -prime ideal in a PMV -subalgebra is the intersection of a · -prime ideal in the overalgebra with the subalgebra. Also, we show that if P is a · -prime ideal of a unital PMV -algebra A and A ′ is a subalgebra of A , having P as a maximal · -ideal, then A ′ / 0 P ( A ) is a local PMV -algebra which is called the localization of A at P relative to A ′ where 0 P ( A ) is the intersection of all · -prime ideals of A contained in P .
ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-017-2690-8