Fixed Points of Affine Maps

Jonathan S. Golan
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Jonathan S. Golan: University of Haifa

Chapter 25 in Semirings and their Applications, 1999, pp 285-306 from Springer

Abstract: Abstract Let R be a semiring and let M be a left R-semimodule. If a ∈ R and m ∈ M then the R-affine map from M to itself defined by a and m is the function λ a , m: M → M given by λ a, m : m′ → am′ + m. We will denote the set of all R-affine maps from M to itself by Aff(M). Note that affine maps are written as acting on the side opposite scalar multiplication, in this case on the right. We can define affine maps of right R-semimodules in a similar fashion: if M is a right R-semimodule, if a ∈ R, and if m ∈ M then we have an R-affine map ρa, m: M → M given by ρ a , m: m′ ↦ m + m′a. These maps will be written as acting on the left.

Keywords: Stability Index; Short Path Problem; Multiplicative Identity; Convergence Domain; Unique Maximal Element (search for similar items in EconPapers)
Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-015-9333-5_25

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DOI: 10.1007/978-94-015-9333-5_25

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