Realization Theorems for Valuated pnp^n-Socles

  • Patrick W. Keef

    Whitman College, Walla Walla, USA


If nn is a positive integer and pp is a prime, then a valuated pnp^n-socle is said to be nn-summable if it is isometric to a valuated direct sum of countable valuated groups. The functions from ω1\omega_1 to the cardinals that can appear as the Ulm function of an nn-summable valuated pnp^n-socle are characterized, as are the nn-summable valuated pnp^n-socles that can appear as the pnp^n-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 nn-summable groups that are uniquely determined by their Ulm functions.

Cite this article

Patrick W. Keef, Realization Theorems for Valuated pnp^n-Socles. Rend. Sem. Mat. Univ. Padova 126 (2011), pp. 151–173

DOI 10.4171/RSMUP/126-9