nLab ordered reduced local ring



An ordered reduced local ring is a local ring which is both an ordered local ring and an reduced local ring: a commutative ring RR with a strict order <\lt such that the positive elements form a multiplicative subset of RR, the sum of two positive elements is positive, every element aRa \in R is invertible if and only if it is positive or negative, and every nilpotent element is equal to zero.


Unlike the theory of ordered fields, the theory of ordered reduced local rings is a coherent theory.

See also

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