分次σ-半单类

The Graded σ-semisimple Class

讨论了分次σ半单类的一些重要性质,给出了分次环类S是分次σ半单类的2个充分必要条件:1)S是分次σ正则的,若分次环R的任何非零分次σ子环都可以分次同态满射到S中非零分次环上,则R∈S;2)S是分次正则的、分次余可归纳的,并且是分次扩张闭的.

The properties of the graded σ-semisimple class are discussed,two necessary and sufficient conditions that the graded ring class S is graded σ-semisimple class are 1) S be graded σ-regular,if any nonzerograded σ-subring of graded ring R may homomorphic epimorphism to nonzero graded ring of S,then R∈S.2) S be graded σ-regular,graded co-inducible and graded extension closed.