Abstract
Let R be a semiring and let M and M’ be left R-semimodules. Each element u of M’ defines a constant function k u : M → M’ given by k u : m → u for each m G M. An affine map from M to M’ is a function from M to M’ of the form ? α,u = α + K u , where α ∈ Hom R (M, M’) and iz u ∈ M’. We will denote the set of all affine maps from M to M’ by Aff R (M,M’). In particular, we see that Hom R (M, M’) ⊆ Aff R (M, M’). Affine maps between left R-semimodules will, like homomorphisms, be written as acting on the right.
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© 2003 Springer Science+Business Media Dordrecht
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Golan, J.S. (2003). Affine maps between semimodules. In: Semirings and Affine Equations over Them: Theory and Applications. Mathematics and Its Applications, vol 556. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0383-3_9
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DOI: https://doi.org/10.1007/978-94-017-0383-3_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6310-6
Online ISBN: 978-94-017-0383-3
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