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Title: Generalized cardinal properties of lattices and lattice ordered groups (English)
Author: Jakubík, Ján
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 54
Issue: 4
Year: 2004
Pages: 1035-1053
Summary lang: English
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Category: math
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Summary: 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. (English)
Keyword: bounded lattice
Keyword: lattice ordered group
Keyword: generalized cardinal property
Keyword: homogeneity
MSC: 06B05
MSC: 06F15
idZBL: Zbl 1080.06029
idMR: MR2100012
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Date available: 2009-09-24T11:19:53Z
Last updated: 2016-04-07
Stable URL: http://hdl.handle.net/10338.dmlcz/127949
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