Let be a groupoid (semigroup,group) and let be a ring (not necessarily with unity) which can be expressed as a of additive subgroups of with . If for all then we say that is groupoid graded (semigroup-graded, group-graded) ring.
Any element in (where ) is said to be homogeneous of degree . Each element can be expressed as a unique and finite sum of homogeneous elements .
For any subset we have . Similarly . If is a subsemigroup of then is a subring of . If is a left (right, two-sided) ideal of then is a left (right, two-sided) ideal of .
|Date of creation||2013-03-22 11:45:03|
|Last modified on||2013-03-22 11:45:03|
|Last modified by||aplant (12431)|
|Defines||groupoid graded ring|
|Defines||semigroup graded ring|
|Defines||group graded ring|