A semiring scheme is like a scheme but where the base commutative ring can be any commutative semiring. Note that we consider the simplest definition of semirings as defined under the name “rig” on the page rig ie. we have an additive unit 0, a multiplicative unit 1 and .
Oliver Lorscheid, The geometry of blueprints: Part I: Algebraic background and scheme theory, Advances in Mathematics, 229 3 (2012) 1804-1846 (pdf, doi:10.1016/j.aim.2011.12.018)
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