Realization Theorems for Valuated -Socles
Patrick W. Keef
Whitman College, Walla Walla, USA
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Abstract
If is a positive integer and is a prime, then a valuated -socle is said to be -summable if it is isometric to a valuated direct sum of countable valuated groups. The functions from to the cardinals that can appear as the Ulm function of an -summable valuated -socle are characterized, as are the -summable valuated -socles that can appear as the -socle of some primary abelian group. The second statement generalizes a classical result of Honda from [9]. Assuming a particular consequence of the generalized continuum hypothesis, a complete description is given of the -summable groups that are uniquely determined by their Ulm functions.
Cite this article
Patrick W. Keef, Realization Theorems for Valuated -Socles. Rend. Sem. Mat. Univ. Padova 126 (2011), pp. 151–173
DOI 10.4171/RSMUP/126-9