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.
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Ā© 1999 Springer Science+Business Media Dordrecht
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Golan, J.S. (1999). Some Constructions for Semimodules. In: Semirings and their Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9333-5_16
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DOI: https://doi.org/10.1007/978-94-015-9333-5_16
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5252-0
Online ISBN: 978-94-015-9333-5
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