nLab ordered Artinian local ring



An ordered Artinian local ring is a local ring which is both an ordered local ring and an Artinian local ring: a commutative ring RR with a strict weak 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 the set of non-invertible elements forms a nilradical.

See also

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