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math.RA2015
Decompositions of modules lacking zero sums
Zur Izhakian, Manfred Knebusch, Louis Rowen
A direct sum decomposition theory is developed for direct summands (and complements) of modules over a semiring , having the property that implies and .…
math.RA2015★ 2 cited
Quadratic and Symmetric Bilinear Forms on Modules with Unique Base Over a Semiring
Zur Izhakian, Manfred Knebusch, Louis Rowen
We study quadratic forms on free modules with unique base, the situation that arises in tropical algebra, and prove the analog of Witt's Cancellation Theorem. Also, the tensor prod…
math.RA2015★ 1 cited
Supertropical Quadratic Forms II
Zur Izhakian, Manfred Knebusch, Louis Rowen
This article is a sequel of [4], where we introduced quadratic forms on a module~ over a supertropical semiring and analysed the set of bilinear companions of a quadratic f…