Keyboard graph navigation: press N for concepts or E for relations; use arrow keys, Home, and End to move; Enter selects; Shift plus Enter selects and centers; plus and minus zoom; zero fits; Escape clears the selection. Use the visible viewport buttons as alternatives to dragging, wheel, and pinch gestures.
Canonical static concept record
Open this concept in the interactive graphRead the Markdown equivalent
An integral domain in which every ideal is generated by one element.
wp-pidnlab-principal-ideal-domainmilne-algebraic-number-theoryEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
The Euclidean algorithm implies every ideal is principal.
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
nlab-euclidean-domainwp-pidmilne-algebraic-number-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Require every ideal to have one generator.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-pidmilne-algebraic-number-theoryEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Require the PID to be a nonfield local ring with a unique nonzero prime ideal (its maximal ideal).
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-dvrmilne-algebraic-number-theory