Priestley dualities for some lattice-ordered algebraic structures, including MTL, IMTL and MV-algebras

Leonardo Cabrer; Sergio Celani

Open Mathematics (2006)

  • Volume: 4, Issue: 4, page 600-623
  • ISSN: 2391-5455

Abstract

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In this work we give a duality for many classes of lattice ordered algebras, as Integral Commutative Distributive Residuated Lattices MTL-algebras, IMTL-algebras and MV-algebras (see page 604). These dualities are obtained by restricting the duality given by the second author for DLFI-algebras by means of Priestley spaces with ternary relations (see [2]). We translate the equations that define some known subvarieties of DLFI-algebras to relational conditions in the associated DLFI-space.

How to cite

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Leonardo Cabrer, and Sergio Celani. "Priestley dualities for some lattice-ordered algebraic structures, including MTL, IMTL and MV-algebras." Open Mathematics 4.4 (2006): 600-623. <http://eudml.org/doc/269542>.

@article{LeonardoCabrer2006,
abstract = {In this work we give a duality for many classes of lattice ordered algebras, as Integral Commutative Distributive Residuated Lattices MTL-algebras, IMTL-algebras and MV-algebras (see page 604). These dualities are obtained by restricting the duality given by the second author for DLFI-algebras by means of Priestley spaces with ternary relations (see [2]). We translate the equations that define some known subvarieties of DLFI-algebras to relational conditions in the associated DLFI-space.},
author = {Leonardo Cabrer, Sergio Celani},
journal = {Open Mathematics},
keywords = {03G10; 03B50; 06D35; 06D72},
language = {eng},
number = {4},
pages = {600-623},
title = {Priestley dualities for some lattice-ordered algebraic structures, including MTL, IMTL and MV-algebras},
url = {http://eudml.org/doc/269542},
volume = {4},
year = {2006},
}

TY - JOUR
AU - Leonardo Cabrer
AU - Sergio Celani
TI - Priestley dualities for some lattice-ordered algebraic structures, including MTL, IMTL and MV-algebras
JO - Open Mathematics
PY - 2006
VL - 4
IS - 4
SP - 600
EP - 623
AB - In this work we give a duality for many classes of lattice ordered algebras, as Integral Commutative Distributive Residuated Lattices MTL-algebras, IMTL-algebras and MV-algebras (see page 604). These dualities are obtained by restricting the duality given by the second author for DLFI-algebras by means of Priestley spaces with ternary relations (see [2]). We translate the equations that define some known subvarieties of DLFI-algebras to relational conditions in the associated DLFI-space.
LA - eng
KW - 03G10; 03B50; 06D35; 06D72
UR - http://eudml.org/doc/269542
ER -

References

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