分次余代数的余理想

The Coideal of Graded Coalgebra

设C是分次余代数,讨论D是C的分次子余代数的充要条件是D的垂直正交补D┴是R的分次理想;D是C的分次余理想的充要条件是D的垂直正交补D┴是R的分次子代数;D是C的分次右(左)余理想的充要条件是D的垂直正交补D┴是R的分次右(左)理想.特别地,分别取D与C的子空间De与Ce,它们也有一定的关系.

In this text,let C be graded coalgebra,the author discusses that D is the graded subcoalgebra of C if only if that D^⊥ is the graded ideal of R ; D is the graded subcoideal of C if only if that D^⊥ is the graded subcoalgebra of R; D is the graded right （left） coideal of C if only if that ^⊥ is the graded right （left） ieal of R. Especially let D, and C, be subspace of D and C ,then the author also discusses the relations between De and Ce.