Statement:

(Where \(p\) is a prime) \(AL21\)\((p)\): Every vector space over \(\mathbb Z_p\) has the property that for every subspace \(S\) of \(V\), there is a subspace \(S'\) of \(V\) such that \(S \cap S' = \{ 0 \}\) and \(S \cup S'\) generates \(V\) in other words such that \(V = S \oplus S'\).   Rubin, H./Rubin, J [1985], p.119, AL21.

Howard_Rubin_Number: 430-p

Parameter(s): This form depends on the following parameter(s): \(p\),

This form's transferability is: Unknown

This form's negation transferability is: Negation Transferable

Article Citations:
Bleicher-1964: Some theorems on vector spaces and the axiom of choice

Book references
Equivalents of the Axiom of Choice II, Rubin, J., 1985

Note connections:

The following forms are listed as conclusions of this form class in rfb1: 67,

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