ON THE MAXIMAL CARDINALITY OF AN INFINITE CHAIN OF VECTOR SUBSPACES

David E. DOBBS

Article Details

ON THE MAXIMAL CARDINALITY OF AN INFINITE CHAIN OF VECTOR SUBSPACES

Authors:

David E. DOBBS

Publisher:

Abdullah HARMANCI

Journal:

International Electronic Journal of Algebra 2013 Vol.13 Issue 13, pp.63-68

Document Type:

Article

Publication Date:

5/2013

Document Language:

Turkish

Document ID (Org No.):

2000718241

Frequency:

Monthly

eISSN:

1306-6048

pISSN:

1306-6048

Abstract:

 

For each infinite cardinal number κ, let Ω(κ) be the supremum of
 the cardinalities of chains of subsets of a set of cardinality κ. (Ω(κ) is equal
 to what has been called ded(κ) in the literature.) Let K be a field and V a
 vector space over K. Let Λ(V ) be the supremum of the cardinalities of chains
 of vector subspaces of V . Let the dimension of V as a vector space over K be
 the infinite cardinal number κ. Then Ω(κ) ≤ Λ(V ) ≤ Ω(|V |), and so Λ(V ) > κ,
 contrary to a result of Menth. If, in addition, K is either finite or infinite with
 |K| ≤ κ, then Ω(κ) = Ω(|V |) (= Λ(V )).

Article Details

ON THE MAXIMAL CARDINALITY OF AN INFINITE CHAIN OF VECTOR SUBSPACES

Authors: David E. DOBBS

Publisher: Abdullah HARMANCI

Journal: International Electronic Journal of Algebra 2013 Vol.13 Issue 13, pp.63-68

Document Type: Article

Publication Date: 5/2013

Document Language: Turkish

Document ID (Org No.): 2000718241

Frequency: Monthly

eISSN: 1306-6048

pISSN: 1306-6048

Issues

Authors:

David E. DOBBS

Publisher:

Abdullah HARMANCI

Journal:

International Electronic Journal of Algebra 2013 Vol.13 Issue 13, pp.63-68

Document Type:

Article

Publication Date:

5/2013

Document Language:

Turkish

Document ID (Org No.):

2000718241

Frequency:

Monthly

eISSN:

1306-6048

pISSN:

1306-6048