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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
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Citations of this work
Representing quantum structures as near semirings.Stefano Bonzio, Ivan Chajda & Antonio Ledda - 2016 - Logic Journal of the IGPL 24 (5).
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.
References found in this work
Perfect MV-algebras are categorically equivalent to abelianl-groups.Antonio Di Nola & Ada Lettieri - 1994 - Studia Logica 53 (3):417-432.
Yosida Type Representation for Perfect MV‐Algebras.Lawrence P. Belluce & Antonio Di Nola - 1996 - Mathematical Logic Quarterly 42 (1):551-563.
Perfect MV-Algebras Are Categorically Equivalent to Abelian l-Groups.Antonio Di Nola & Ada Lettieri - 1994 - Studia Logica 53 (3):417-432.
Yosida Type Representation for Perfect MV-Algebras.Lawrence Belluce & Antonio di Nola - 1996 - Mathematical Logic Quarterly 42 (1):551-563.
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