J-半交换环的进一步探讨

Further Discussions on J-semicommutative Rings

证明了若R/I是J-半交换环,则R也是J-半交换环,这里I是R的理想,且I■J(R).根据这个结果,证明了Hurwitz级数环H(R)是J-半交换环当且仅当R是J-半交换环;环R上的斜幂级数环R[[x;α]]是J-半交换环当且仅当R是J-半交换环;群环RG是J-半交换环当且仅当R是J-半交换环,这里G是P-群,Char R=p^s(s≥1),p是素数.

It is proved that if R/I is a J-semicommutative ring,then R is also a J-semicommutative ring,where I is the ideal of R,and I■J(R).According to this result,we could prove the following:firstly,a ring of Hurwitz series H(R)is a J-semicommutative ring if and only if R is a J-semicommutative ring;secondly,a skew power series ring R[[x;α]]over R is a J-semicommutative ring if and only if R is a J-semicommutative ring;lastly,a group ring RG is a J-semicommutative ring if and only if R is a J-semicommutative ring,where G is a P-group,Char R=p^s(s≥1),p is a prime.