weakest extension of a partial ordering
Let be a commutative ring with partial ordering and suppose that is a ring that admits a partial ordering. If is a ring monomorphism (thus we regard as an over-ring of ), then any partial ordering of that can contain will also contain the set defined by
is itself a partial ordering and it is called the weakest partial ordering of that extends (through ). It is called ”weakest” because this is the smallest partial ordering of that will transform into a poring monomorphism (i.e. a monomorphism in the category of partially ordered rings) (for simplicity, we abuse the symbol here).
|Title||weakest extension of a partial ordering|
|Date of creation||2013-03-22 18:51:40|
|Last modified on||2013-03-22 18:51:40|
|Last modified by||jocaps (12118)|
|Defines||weakest extension of a partial ordering|