# Semilattices with sectional mappings

Ivan Chajda; Günther Eigenthaler

Discussiones Mathematicae - General Algebra and Applications (2007)

- Volume: 27, Issue: 1, page 11-19
- ISSN: 1509-9415

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topIvan Chajda, and Günther Eigenthaler. "Semilattices with sectional mappings." Discussiones Mathematicae - General Algebra and Applications 27.1 (2007): 11-19. <http://eudml.org/doc/276909>.

@article{IvanChajda2007,

abstract = {We consider join-semilattices with 1 where for every element p a mapping on the interval [p,1] is defined; these mappings are called sectional mappings and such structures are called semilattices with sectional mappings. We assign to every semilattice with sectional mappings a binary operation which enables us to classify the cases where the sectional mappings are involutions and / or antitone mappings. The paper generalizes results of [3] and [4], and there are also some connections to [1].},

author = {Ivan Chajda, Günther Eigenthaler},

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

keywords = {semilattice; sectional mapping; antitone mapping; switching mapping; involution},

language = {eng},

number = {1},

pages = {11-19},

title = {Semilattices with sectional mappings},

url = {http://eudml.org/doc/276909},

volume = {27},

year = {2007},

}

TY - JOUR

AU - Ivan Chajda

AU - Günther Eigenthaler

TI - Semilattices with sectional mappings

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2007

VL - 27

IS - 1

SP - 11

EP - 19

AB - We consider join-semilattices with 1 where for every element p a mapping on the interval [p,1] is defined; these mappings are called sectional mappings and such structures are called semilattices with sectional mappings. We assign to every semilattice with sectional mappings a binary operation which enables us to classify the cases where the sectional mappings are involutions and / or antitone mappings. The paper generalizes results of [3] and [4], and there are also some connections to [1].

LA - eng

KW - semilattice; sectional mapping; antitone mapping; switching mapping; involution

UR - http://eudml.org/doc/276909

ER -

## References

top- [1] J.C. Abbott, Semi-Boolean algebras, Matem. Vestnik 4 (1967), 177-198. Zbl0153.02704
- [2] I. Chajda, G. Eigenthaler and H. Länger, Congruence Classes in Universal Algebra, Heldermann Verlag, Lemgo 2003, pp. 217. Zbl1014.08001
- [3] I. Chajda and P. Emanovský, Bounded lattices with antitone involutions and properties of MV-algebras, Discussiones Mathem., General Algebra and Appl. 24 (1) (2004), 31-42. Zbl1082.03055
- [4] I. Chajda, R. Halaš and J. Kühr, Distributive lattices with sectionally antitone involutions, Acta Sci. Math. (Szeged) 71 (2005), 19-33. Zbl1099.06006