On monadic quantale algebras: basic properties and representation theorems

Sergey A. Solovyov

Discussiones Mathematicae - General Algebra and Applications (2010)

  • Volume: 30, Issue: 1, page 91-118
  • ISSN: 1509-9415

Abstract

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Motivated by the concept of quantifier (in the sense of P. Halmos) on different algebraic structures (Boolean algebras, Heyting algebras, MV-algebras, orthomodular lattices, bounded distributive lattices) and the resulting notion of monadic algebra, the paper introduces the concept of a monadic quantale algebra, considers its properties and provides several representation theorems for the new structures.

How to cite

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Sergey A. Solovyov. "On monadic quantale algebras: basic properties and representation theorems." Discussiones Mathematicae - General Algebra and Applications 30.1 (2010): 91-118. <http://eudml.org/doc/276697>.

@article{SergeyA2010,
abstract = {Motivated by the concept of quantifier (in the sense of P. Halmos) on different algebraic structures (Boolean algebras, Heyting algebras, MV-algebras, orthomodular lattices, bounded distributive lattices) and the resulting notion of monadic algebra, the paper introduces the concept of a monadic quantale algebra, considers its properties and provides several representation theorems for the new structures.},
author = {Sergey A. Solovyov},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {m-semilattice; ⋁-lattice; quantale; quantale module; topological system; tropological system; quantale algebra; quantaloid; quantale algebroid; quantifier; monadic quantale algebra; Girard quantale; Q-equivalence relation; Ω-valued set; GL-monoid; commutative integral cl-monoid; m-semilattices},
language = {eng},
number = {1},
pages = {91-118},
title = {On monadic quantale algebras: basic properties and representation theorems},
url = {http://eudml.org/doc/276697},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Sergey A. Solovyov
TI - On monadic quantale algebras: basic properties and representation theorems
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2010
VL - 30
IS - 1
SP - 91
EP - 118
AB - Motivated by the concept of quantifier (in the sense of P. Halmos) on different algebraic structures (Boolean algebras, Heyting algebras, MV-algebras, orthomodular lattices, bounded distributive lattices) and the resulting notion of monadic algebra, the paper introduces the concept of a monadic quantale algebra, considers its properties and provides several representation theorems for the new structures.
LA - eng
KW - m-semilattice; ⋁-lattice; quantale; quantale module; topological system; tropological system; quantale algebra; quantaloid; quantale algebroid; quantifier; monadic quantale algebra; Girard quantale; Q-equivalence relation; Ω-valued set; GL-monoid; commutative integral cl-monoid; m-semilattices
UR - http://eudml.org/doc/276697
ER -

References

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