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Decompositions of modules lacking zero sums

Izhakian, Zur ; Knebusch, Manfred ; Rowen, Louis



Abstract

A module over a semiring lacks zero sums (LZS) if it has the property that v +w = 0 implies v = 0 and w = 0. While modules over a ring never lack zero sums, this property always holds for modules over an idempotent semiring and related semirings, so arises for example in tropical mathematics. A direct sum decomposition theory is developed for direct summands (and complements) of LZS modules: The ...

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