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Summand absorbing submodules of a module over a semiring

Izhakian, Zur ; Knebusch, Manfred ; Rowen, Louis



Abstract

An R-module V over a semiring R lacks zero sums (LZS) if x + y = 0 implies x = y = 0. More generally, we call a submodule W of V "summand absorbing" (SA) in V if for all x, y is an element of V : x + y is an element of W double right arrow x is an element of W, y is an element of W. These arise in tropical algebra and modules over idempotent semirings, as well as modules over semirings of sums of ...

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