分次环上的分次Brown-McCoy根

Graded Brown - McCoy Radicals of Graded Rings

通过引入弱g-正则元的概念,对于无单位元分次环R,给出以内部元素刻画的分次Brown—McCoy根BMG(R).证明了任何分次环都有1个分次Brown—McCoy根,并且当R有1时,BMG(R)即为通常定义的BMgr(R).另外还证明了BMc(R)具有遗传性.

The notion of weakly g - regular element is introducted and a definition of graded Brown -McCoy radical is given by element property for general monoid graded rings(not necessarily with 1). That every graded ring must have a graded Brown - McCoy radical is proved. BMG(R) which is equal to the usual BMgr(R) when R has1.By the way,that BMG(.R) is a hereditary radical is got.