General p-valuations on abelian groups |
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| Authors: | David M Arnold Fred Richman Charles I Vinsonhaler |
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| Institution: | 1. New Mexico State University , Las Cruces, NM, 88003;2. Baylor University , Waco, TX, 76798current address;3. Florida Atlantic University , Boca Raton, FL, 33431current address;4. University of Connecticut , Storrs, CT, 06268 |
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| Abstract: | A subgroup of a p-group is valuated in a natural way, and every valuated p-group can be embedded as a valuated subgroup of a p-group. We generalize this theorem to subgroups of p-valuated groups with values in an arbitrary value domain D. The induced valuation on the subgroup assigns to each element an equivalence class of D-valuated rooted trees. In the classical caseD is trivial and the equivalence class of trees can be identified with an extended ordinal. The embedding is functorial if some set-theoretic problems can be overcome, which they can be if D is trivial or equal to the ordinals. |
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