# Interior and closure operators on bounded commutative residuated l-monoids

Discussiones Mathematicae - General Algebra and Applications (2008)

- Volume: 28, Issue: 1, page 11-27
- ISSN: 1509-9415

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topJiří Rachůnek, and Filip Švrček. "Interior and closure operators on bounded commutative residuated l-monoids." Discussiones Mathematicae - General Algebra and Applications 28.1 (2008): 11-27. <http://eudml.org/doc/276908>.

@article{JiříRachůnek2008,

abstract = {Topological Boolean algebras are generalizations of topological spaces defined by means of topological closure and interior operators, respectively. The authors in [14] generalized topological Boolean algebras to closure and interior operators of MV-algebras which are an algebraic counterpart of the Łukasiewicz infinite valued logic. In the paper, these kinds of operators are extended (and investigated) to the wide class of bounded commutative Rl-monoids that contains e.g. the classes of BL-algebras (i.e., algebras of the Hájek's basic fuzzy logic) and Heyting algebras as proper subclasses.},

author = {Jiří Rachůnek, Filip Švrček},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {residuated l-monoid; residuated lattice; closure operator; BL-algebra; MV-algebra},

language = {eng},

number = {1},

pages = {11-27},

title = {Interior and closure operators on bounded commutative residuated l-monoids},

url = {http://eudml.org/doc/276908},

volume = {28},

year = {2008},

}

TY - JOUR

AU - Jiří Rachůnek

AU - Filip Švrček

TI - Interior and closure operators on bounded commutative residuated l-monoids

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2008

VL - 28

IS - 1

SP - 11

EP - 27

AB - Topological Boolean algebras are generalizations of topological spaces defined by means of topological closure and interior operators, respectively. The authors in [14] generalized topological Boolean algebras to closure and interior operators of MV-algebras which are an algebraic counterpart of the Łukasiewicz infinite valued logic. In the paper, these kinds of operators are extended (and investigated) to the wide class of bounded commutative Rl-monoids that contains e.g. the classes of BL-algebras (i.e., algebras of the Hájek's basic fuzzy logic) and Heyting algebras as proper subclasses.

LA - eng

KW - residuated l-monoid; residuated lattice; closure operator; BL-algebra; MV-algebra

UR - http://eudml.org/doc/276908

ER -

## References

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