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Decomposition of Elements in Abelian Groups
| Content Provider | Semantic Scholar |
|---|---|
| Author | Oldenburger, Rufus T. |
| Copyright Year | 2007 |
| Abstract | In the present paper we determine necessary and sufficient conditions for an abelian group to have the property Pw . The author first proved the validity of these conditions for fields, but, as noted by T. Nakayama, the operation X does not occur, so that the theory may be stated for a system of elements with only one operation + defined for these elements. Groups with the property Pn have useful algebraic applications.! One is naturally led to consider the decomposability of any given element of a group G into a sum of distinct elements of G. This problem is treated in §3. I t is necessary in the treatment of decompositions of elements to distinguish only between nonzero elements of order 2, elements of order different from 2, and the zero element. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.ams.org/journals/bull/1939-45-02/S0002-9904-1939-06926-7/S0002-9904-1939-06926-7.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Arabic numeral 0 Linear algebra |
| Content Type | Text |
| Resource Type | Article |
