# 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

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topLeonardo 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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