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Some Constructions for Semimodules

In: Semirings and their Applications

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  • Jonathan S. Golan

    (University of Haifa)

Abstract

In this chapter we present three basic constructions associated with semimodules. The first of these, the construction of the module of differences of an R-semimodule, is based on the corresponding construction for semirings. The other two, decomposition of a semimodule into a direct sum of indecomposable summands and the construction of the tensor product of semimodules, are inspired by the corresponding constructions for modules over a ring. In each case, however, the results differ somewhat from those in module theory due to the allowances we have to make for being in a semimodule environment.

Suggested Citation

  • Jonathan S. Golan, 1999. "Some Constructions for Semimodules," Springer Books, in: Semirings and their Applications, chapter 16, pages 181-190, Springer.
    • Handle: RePEc:spr:sprchp:978-94-015-9333-5_16
    DOI: 10.1007/978-94-015-9333-5_16
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