NDLI: Rings and Gödel algebras

Content Provider	Springer Nature Link
Author	Marchioni, Enrico Belluce, L. P. Di la, Antonio
Copyright Year	2010
Abstract	In this paper, we study those rings whose semiring of ideals can be given the structure of a Gödel algebra. Such rings are called Gödel rings. We investigate such structures both from an algebraic and a topological point of view.Our main result states that every Gödel ring R is a subdirect product of prime Gödel rings R i, and the Gödel algebra Id(R) associated to R is subdirectly embeddable as an algebraic lattice into $${{\prod_{i}}Id(R_{i})}$$ , where each Id(R i) is the algebraic lattice of ideals of R i that can be equipped with the structure of a Gödel algebra. We see that the mapping associating to each Gödel ring its Gödel algebra of ideals is functorial from the category of Gödel rings with epimorphisms into the full subcategory of frames whose objects are Gödel algebras and whose morphisms are complete epimorphisms.
Ending Page	116
Page Count	14
Starting Page	103
File Format	PDF
ISSN	00025240
e-ISSN	14208911
Journal	algebra universalis
Issue Number	1
Volume Number	64
Language	English
Publisher	SP Birkhäuser Verlag Basel
Publisher Date	2010-11-11
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Von Neumann regular rings Algebra Gödel algebras von Neumann regular rings and generalizations Heyting algebras Monoid of ideals Noncommutative rings
Content Type	Text
Resource Type	Article
Subject	Logic Algebra and Number Theory

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Rings and Gödel algebras