# A decomposition of homomorphic images of nearlattices

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2006)

- Volume: 45, Issue: 1, page 43-51
- ISSN: 0231-9721

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topChajda, Ivan, and Kolařík, Miroslav. "A decomposition of homomorphic images of nearlattices." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 45.1 (2006): 43-51. <http://eudml.org/doc/32503>.

@article{Chajda2006,

abstract = {By a nearlattice is meant a join-semilattice where every principal filter is a lattice with respect to the induced order. The aim of our paper is to show for which nearlattice $\mathcal \{S\}$ and its element $c$ the mapping $\varphi _c(x) = \langle x \vee c, x \wedge _p c \rangle $ is a (surjective, injective) homomorphism of $\mathcal \{S\}$ into $[c) \times (c]$.},

author = {Chajda, Ivan, Kolařík, Miroslav},

journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},

keywords = {nearlattice; semilattice; distributive element; pseudocomplement; dual pseudocomplement; nearlattice; semilattice; distributive element; dual pseudocomplement},

language = {eng},

number = {1},

pages = {43-51},

publisher = {Palacký University Olomouc},

title = {A decomposition of homomorphic images of nearlattices},

url = {http://eudml.org/doc/32503},

volume = {45},

year = {2006},

}

TY - JOUR

AU - Chajda, Ivan

AU - Kolařík, Miroslav

TI - A decomposition of homomorphic images of nearlattices

JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

PY - 2006

PB - Palacký University Olomouc

VL - 45

IS - 1

SP - 43

EP - 51

AB - By a nearlattice is meant a join-semilattice where every principal filter is a lattice with respect to the induced order. The aim of our paper is to show for which nearlattice $\mathcal {S}$ and its element $c$ the mapping $\varphi _c(x) = \langle x \vee c, x \wedge _p c \rangle $ is a (surjective, injective) homomorphism of $\mathcal {S}$ into $[c) \times (c]$.

LA - eng

KW - nearlattice; semilattice; distributive element; pseudocomplement; dual pseudocomplement; nearlattice; semilattice; distributive element; dual pseudocomplement

UR - http://eudml.org/doc/32503

ER -

## References

top- Chajda I., Kolařík M., Nearlattices, Discrete Math., submitted. Zbl1151.06004MR2446101
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- Grätzer G.: General Lattice Theory., Birkhäuser Verlag, Basel, , 1978. (1978) MR0504338
- Noor A. S. A., Cornish W. H., Multipliers on a nearlattices, Comment. Math. Univ. Carol. (1986), 815–827. (1986) MR0874675
- Scholander M., Trees, lattices, order and betweenness, Proc. Amer. Math. Soc. 3 (1952), 369–381. (1952) MR0048405
- Scholander M., Medians and betweenness, Proc. Amer. Math. Soc. 5 (1954), 801–807. (1954) MR0064749
- Scholander M., Medians, lattices and trees, Proc. Amer. Math. Soc. 5 (1954), 808–812. (1954) MR0064750

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