corner of a ring
It’s not hard to see that is a ring with as its multiplicative identity:
is the additive inverse of in ,
, with , for any .
If has no multiplicative identity, then any corner of is a proper subset of which is a ring and not a subring of . If has 1 as its multiplicative identity and if is an idempotent, then the is not a subring of as they don’t share the same multiplicative identity. In this case, the corner is said to be proper. If we set , then is also a proper corner of .
- 1 I. Kaplansky, Rings of Operators, W. A. Benjamin, Inc., New York, 1968.
|Title||corner of a ring|
|Date of creation||2013-03-22 15:43:56|
|Last modified on||2013-03-22 15:43:56|
|Last modified by||CWoo (3771)|