Английская Википедия:Dedekind-finite ring
Материал из Онлайн справочника
Шаблон:Short description In mathematics, a ring is said to be a Dedekind-finite ring if ab = 1 implies ba = 1 for any two ring elements a and b. In other words, all one-sided inverses in the ring are two-sided.
These rings have also been called directly finite rings[1] and von Neumann finite rings.[2]
Properties
- Any finite ring is Dedekind-finite.[2]
- Any subring of a Dedekind-finite ring is Dedekind-finite.[1]
- Any domain is Dedekind-finite.[2]
- Any left Noetherian ring is Dedekind-finite.[2]
- A unit-regular ring is Dedekind-finite.[2]
- A local ring is Dedekind-finite.[2]
References
See also
