Subadditive functions on modules and subgroups of Abelian groups (Q1118108)

The author studies the extension problem for subadditive functions. He proves, among others, that if A is an ordered abelian group, \(A_+=\{x\in A| x\geq 0\}\) and M, \(M^*\) are modules in A with \(M\subset M^*\subset A_+\), then a subadditive function g: \(M\to {\mathbb{R}}\) can be extended to a subadditive function on \(M^*\) whenever \(card(M)=\aleph_ 0\) and\(card(M^*)\leq \aleph_ 1.\) Cases where such extensions do not exist are also discussed. Finally the author shows that every real-valued subadditive function g on an abelian group admits a representation \(g=\lambda +\phi\) where \(\lambda\) is additive and \(\phi\) is subadditive and non-negative.