symmetric monoidal (∞,1)-category of spectra
A pseudolattice ordered ring is an partially ordered ring whose partial order forms a pseudolattice.
A psuedolattice ordered ring is a preordered ring where the partial order is a pseudolattice: it has binary joins and meets.
If the relation is only a preorder, then the preordered ring is said to be a pseudolattice preordered ring.
The following essentially algebraic definition is adapted from the algebraic definition of pseudolattice ordered abelian group by Peter Freyd:
A pseudolattice ordered ring is an ring with a function such that for all and in ,
and the following Horn clause:
An element in is non-negative if . The Horn clause can then be stated as multiplication of non-negative elements is non-negative.
The join is defined as
the meet is defined as
and the absolute value is defined as
The order relation is defined as in all pseudolattices: if .
All totally ordered rings, such as the integers, the rational numbers, and the real numbers, are pseudolattice ordered rings.
Last revised on December 7, 2022 at 15:58:47. See the history of this page for a list of all contributions to it.