Power Algebras over Semirings: With Applications in Mathematics and Computer Science / Edition 1

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Overview

This research monograph investigates sets of the form RA where R is a semiring, and A is a set with a certain structure. Such constructs gen eralise fuzzy and toll algebraic structures, which in recent years hav e shown themselves of importance in engineering and computer science, as well as in new mathematical disciplines like idempotent analysis. T his volume puts much of the ad hoc work of the past decade on a firm m athematical foundation by creating a unified approach which has import ant implications in such diverse areas as formal language theory, disc rete dynamical systems, models of optimal control, and many others.

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Product Details

  • ISBN-13: 9780792358343
  • Publisher: Springer Netherlands
  • Publication date: 7/31/1999
  • Series: Mathematics and Its Applications (closed) Series , #488
  • Edition description: 1999
  • Edition number: 1
  • Pages: 206
  • Product dimensions: 0.63 (w) x 9.21 (h) x 6.14 (d)

Table of Contents

Preface. Some (hopefully) motivating examples. 0. Background material. 1. Powers of a semiring. 2. Relations with values in a semiring. 3. Change of base semirings. 4. Convolutions. 5. Semiring-valued subsemigroups and submonoids. 6. Semiring-valued groups. 7. Semiring-valued submodules and subspaces. 8. Semiring-ideals in semirings and rings. References. Index.

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