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math.RA2012★ 4 cited
Categories of layered semirings
Zur Izhakian, Manfred Knebusch, Louis Rowen
We generalize the constructions of [17,19] to layered semirings, in order to enrich the structure and provide finite examples for applications in arithmetic (including finite examp…
math.RA2012★ 7 cited
Categorical notions of layered tropical algebra and geometry
Zur Izhakian, Manfred Knebusch, Louis Rowen
This paper supplements [17], showing that categorically the layered theory is the same as the theory of ordered monoids (e.g. the max-plus algebra) used in tropical mathematics. A…