- New
-
Topics
- All Categories
- Metaphysics and Epistemology
- Value Theory
- Science, Logic, and Mathematics
- Science, Logic, and Mathematics
- Logic and Philosophy of Logic
- Philosophy of Biology
- Philosophy of Cognitive Science
- Philosophy of Computing and Information
- Philosophy of Mathematics
- Philosophy of Physical Science
- Philosophy of Social Science
- Philosophy of Probability
- General Philosophy of Science
- Philosophy of Science, Misc
- History of Western Philosophy
- Philosophical Traditions
- Philosophy, Misc
- Other Academic Areas
- Journals
- Submit material
- More
Commutative rings whose ideals form an MV-algebra
Mathematical Logic Quarterly 55 (5):468-486 (2009)
Abstract
In this work we introduce a class of commutative rings whose defining condition is that its lattice of ideals, augmented with the ideal product, the semi-ring of ideals, is isomorphic to an MV-algebra. This class of rings coincides with the class of commutative rings which are direct sums of local Artinian chain rings with unitMy notes
Similar books and articles
Commutative rings whose ideals form an MV‐algebra.Lawrence P. Belluce & Antonio Di Nola - 2009 - Mathematical Logic Quarterly 55 (5):468-486.
Rings which admit elimination of quantifiers.Bruce I. Rose - 1978 - Journal of Symbolic Logic 43 (1):92-112.
Lazy bases: a minimalist constructive theory of Noetherian rings.Hervé Perdry - 2008 - Mathematical Logic Quarterly 54 (1):70-82.
Towards the decidability of the theory of modules over finite commutative rings.Gena Puninski & Carlo Toffalori - 2009 - Annals of Pure and Applied Logic 159 (1-2):49-70.
Diophantine properties of finite commutative rings.Mihai Prunescu - 2003 - Archive for Mathematical Logic 42 (3):293-302.
A hierarchy of tree-automatic structures.Olivier Finkel & Stevo Todorčević - 2012 - Journal of Symbolic Logic 77 (1):350-368.
Finitely generated ideals in directed commutative bck-algebra.Barbara Wozniakowska - 1980 - Bulletin of the Section of Logic 9 (4):166-169.
On Boolean algebras and integrally closed commutative regular rings.Misao Nagayama - 1992 - Journal of Symbolic Logic 57 (4):1305-1318.
Representation theory of MV-algebras.Eduardo J. Dubuc & Yuri A. Poveda - 2010 - Annals of Pure and Applied Logic 161 (8):1024-1046.
Ideals in BCK-algebras which are lower semilattices.Marek Palasinski - 1981 - Bulletin of the Section of Logic 10 (1):48-50.
Existentially closed models of the theory of artinian local rings.Hans Schoutens - 1999 - Journal of Symbolic Logic 64 (2):825-845.
Diophantine equivalence and countable rings.Alexandra Shlapentokh - 1994 - Journal of Symbolic Logic 59 (3):1068-1095.
Algebra and logic: papers from the 1974 summer research institute of the Australian Mathematical Society, Monash University, Australia.John N. Crossley (ed.) - 1975 - New York: Springer Verlag.
Hyper MV -ideals in hyper MV -algebras.Lida Torkzadeh & Afsaneh Ahadpanah - 2010 - Mathematical Logic Quarterly 56 (1):51-62.
The model theory of unitriangular groups.Oleg V. Belegradek - 1994 - Annals of Pure and Applied Logic 68 (3):225-261.
Analytics
Added to PP
2017-02-17
Downloads
6 (#1,454,046)
6 months
1 (#1,469,469)
2017-02-17
Downloads
6 (#1,454,046)
6 months
1 (#1,469,469)
Historical graph of downloads
Citations of this work
A non-commutative generalization of Łukasiewicz rings.Albert Kadji, Celestin Lele & Jean B. Nganou - 2016 - Journal of Applied Logic 16:1-13.
BL-rings.O. A. Heubo-Kwegna, C. Lele, S. Ndjeya & J. B. Nganou - 2018 - Logic Journal of the IGPL 26 (3):290-299.
PhilPapers logo by Andrea Andrews and Meghan Driscoll.
This site uses cookies and Google Analytics (see our terms & conditions for details regarding the privacy implications). Use of this site is subject to terms & conditions.
All rights reserved by The PhilPapers Foundation
Server: philpapers-web-55b469568f-bl6rh uwo