Generalized cardinal properties of lattices and lattice ordered groups

Ján Jakubík

Czechoslovak Mathematical Journal (2004)

  • Volume: 54, Issue: 4, page 1035-1053
  • ISSN: 0011-4642

Abstract

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We denote by K the class of all cardinals; put K ' = K ∪ { ∞ } . Let 𝒞 be a class of algebraic systems. A generalized cardinal property f on 𝒞 is defined to be a rule which assings to each A ∈ 𝒞 an element f A of K ' such that, whenever A 1 , A 2 ∈ 𝒞 and A 1 ≃ A 2 , then f A 1 = f A 2 . In this paper we are interested mainly in the cases when (i) 𝒞 is the class of all bounded lattices B having more than one element, or (ii) 𝒞 is a class of lattice ordered groups.

How to cite

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Jakubík, Ján. "Generalized cardinal properties of lattices and lattice ordered groups." Czechoslovak Mathematical Journal 54.4 (2004): 1035-1053. <http://eudml.org/doc/30919>.

@article{Jakubík2004,
abstract = {We denote by $K$ the class of all cardinals; put $K^\{\prime \}= K \cup \lbrace \infty \rbrace $. Let $\mathcal \{C\}$ be a class of algebraic systems. A generalized cardinal property $f$ on $\mathcal \{C\}$ is defined to be a rule which assings to each $A \in \mathcal \{C\}$ an element $f A$ of $K^\{\prime \}$ such that, whenever $A_1, A_2 \in \mathcal \{C\}$ and $A_1 \simeq A_2$, then $f A_1 =f A_2$. In this paper we are interested mainly in the cases when (i) $\mathcal \{C\}$ is the class of all bounded lattices $B$ having more than one element, or (ii) $\mathcal \{C\}$ is a class of lattice ordered groups.},
author = {Jakubík, Ján},
journal = {Czechoslovak Mathematical Journal},
keywords = {bounded lattice; lattice ordered group; generalized cardinal property; homogeneity; bounded lattice; lattice-ordered group; generalized cardinal property; homogeneity},
language = {eng},
number = {4},
pages = {1035-1053},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generalized cardinal properties of lattices and lattice ordered groups},
url = {http://eudml.org/doc/30919},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Jakubík, Ján
TI - Generalized cardinal properties of lattices and lattice ordered groups
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 4
SP - 1035
EP - 1053
AB - We denote by $K$ the class of all cardinals; put $K^{\prime }= K \cup \lbrace \infty \rbrace $. Let $\mathcal {C}$ be a class of algebraic systems. A generalized cardinal property $f$ on $\mathcal {C}$ is defined to be a rule which assings to each $A \in \mathcal {C}$ an element $f A$ of $K^{\prime }$ such that, whenever $A_1, A_2 \in \mathcal {C}$ and $A_1 \simeq A_2$, then $f A_1 =f A_2$. In this paper we are interested mainly in the cases when (i) $\mathcal {C}$ is the class of all bounded lattices $B$ having more than one element, or (ii) $\mathcal {C}$ is a class of lattice ordered groups.
LA - eng
KW - bounded lattice; lattice ordered group; generalized cardinal property; homogeneity; bounded lattice; lattice-ordered group; generalized cardinal property; homogeneity
UR - http://eudml.org/doc/30919
ER -

References

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