On Complete Semimodules1
نویسندگان
چکیده
1. In the first theorem of [3], Wiegandt incorrectly states that a semimodule is complete if and only if it is divisible. (See §2 for definitions.) In this paper we show (in §3) that his theorem should read: a semimodule is complete if and only if it is a divisible group. Divisible semimodules which are not necessarily groups are discussed in §4, in connection with Wiegandt's second theorem. It is shown that a weakly integrally closed, divisible semimodule can be expressed as the direct sum of a divisible (abelian) group and a cone in a rational vector space. The author wishes to acknowledge his gratitude to Professor A. H. Clifford for his many valuable comments.
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