nLab ordered local integral domain



An ordered local integral domain is a local ring which is both an ordered local ring and a local integral domain: 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 if the product of two elements is equal to zero, than one of the two elements is equal to zero.


Unlike the theory of ordered fields, the theory of ordered local integral domains is a coherent theory.

See also

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