In classical mathematics, a multiplicatively cancellable rig is a rig such that each is multiplicatively cancellable.
An element where is a rig is left multiplicatively cancellable iff for every we have that and it is right multiplicatively cancellable iff for every we have that . An element is multiplicatively cancellable iff it is left multiplicatively cancellable and right multiplicatively cancellable.
If is a commutative rig, an element is left multiplicatively cancellable iff it is right multiplicatively cancellable.
Like in the case for integral domains and fields, the definition above bifurcates into multiple definitions in constructive mathematics.
definitions to be ported over
A residue multiplicatively cancellable rig is a rig such that for all , if is not multiplicatively cancellable, then .
A Heyting multiplicatively cancellable rig is a rig with a tight apartness relation such that each is multiplicatively cancellable.
Last revised on August 3, 2022 at 20:28:29. See the history of this page for a list of all contributions to it.