Structure Spaces of Maximal l-Ideals of Lattice-Ordered Rings

Ma, Jingjing; Wojciechowski, Piotr J.

doi:10.1007/978-1-4757-3627-4_14

Cited by 6 publications

(3 citation statements)

References 8 publications

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“…The notion of semisimple f -algebra is present in literature in different forms, due to the different kind of radicals that can be defined on a f -ring (see for example [1,Section 8.6]). We will follow [17], and define an f -algebra ℓ-semisimple if the intersection of all maximal ℓ-ideals is {0}. Definition 3.1.…”

Section: Semisimple and Archimedean F Mv-algebrasmentioning

confidence: 99%

Towards understanding the Pierce–Birkhoff conjecture via MV-algebras

Lapenta

Leustean

2015

Fuzzy Sets and Systems

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Our main issue was to understand the connection between Łukasiewicz logic with product and the Pierce-Birkhoff conjecture, and to express it in a mathematical way. To do this we define the class of f MV-algebras, which are MV-algebras endowed with both an internal binary product and a scalar product with scalars from [0, 1]. The proper quasi-variety generated by [0, 1], with both products interpreted as the real product, provides the desired framework: the normal form theorem of its corresponding logical system can be seen as a local version of the Pierce-Birkhoff conjecture.

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Section: Semisimple and Archimedean F Mv-algebrasmentioning

confidence: 99%

Towards understanding the Pierce–Birkhoff conjecture via MV-algebras

Lapenta

Leustean

2015

Fuzzy Sets and Systems

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“…Johnson showed that the maximal -ideals and maximal left (right) -ideals of a unital f-ring coincide. In [12], it has been shown that in an -unital -reduced -ring, maximal -ideals and maximal left (right) -ideals are in one-to-one correspondence. The following result shows that maximal -ideals and maximal left (right) -ideals in a unital -reduced -algebra with a d-basis coincide.…”

Section: Theorem 53 Let a Be A Unital -Reduced Finite-dimensional -mentioning

confidence: 98%

Lattice-ordered algebras with a d-basis

Ma¹

2006

Journal of Algebra

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“…The approach taken in [HK91] is more likely to be applicable to general f-rings than earlier work. A substantial step forward in the study of structure spaces has been made by J. Ma and P. Wojciechowski in [MW02] where they generalize a theorem of H. Subramanian [Su68] that applies only to commutative J-rings as follows. Suppose Rand 5 are two f-rings with strictly positive identity elements whose only nilpotent element is 0, and such that the intersection of their maximal f-ideals is zero.…”

Section: [2mentioning

confidence: 99%

Ordered Algebraic Structures

Powell¹,

Tsinakis²

2002

Developments in Mathematics

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Editors of conference proceedings are urged to include a few survey papers for wider appeal. Research monographs which could be used as texts or references for graduate level courses would also be suitable for the series. Contributed volumes are those where various authors either write papers or chapters in an organized volume devoted to a topic of special/current interest or importance. A contributed volume could deal with a classical topic which is once again in the limelight owing to new developments.

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Structure Spaces of Maximal l-Ideals of Lattice-Ordered Rings

Cited by 6 publications

References 8 publications

Towards understanding the Pierce–Birkhoff conjecture via MV-algebras

Towards understanding the Pierce–Birkhoff conjecture via MV-algebras

Lattice-ordered algebras with a d-basis

Ordered Algebraic Structures

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