We get some useful characters of right a - module , and find an index set ( q ) , q = 1 - 1a , is a system of finitely generated projec - tive generators of gr - ( a , ) for some - graded rings . results , we give the definition of semigroup gr - faithfully balanced 第二部分,对于半群我们给出如下定义:得到了半群分次右模上的一些性质,找到了半群分次右模的有限生成投射生成子,其中,并定义了半群分次?忠实?平衡模。
Graded triangular extensions and graded trivial extensions over a ring are defined respectively , and the relation between them with grade morita dualities and their initial subrings with morita dualities is discussed . the graded selfduality of a polynomial ring in multivariables over a cogenerator ring as a graded ring of type different group i ?讨论了余生成子环上的多元多项式环作为不同群的分次环的分次自对偶问题,并证明了有自对偶的环的一种特殊的分次三角扩张有分次自对偶