The Upper Central Chain of a Radical Ring

Ｔｈｒｏｕｇｈｏｕｔ,ＲｉｓａＪａｃｏｂｓｏｎｒａｄｉｃａｌｒｉｎｇ,ａｎｄｄｅｆｉｎｅａ ｂ =ａ +ｂ -ａｂａｎｄ [ａ ,ｂ] =ａｂ-ｂａｆｏｒａｎｙａ ,ｂ∈Ｒ .Ｔｈｅｎ (Ｒ , )ｉｓａｇｒｏｕｐｗｉｔｈｉｄｅｎｔｉｔｙ 0 ,ｃａｌｌｅｄｔｈｅａｄｊｏｉｎｔｏｒｃｉｒｃｌｅｇｒｏｕｐｏｆＲ ,ａｎｄ (Ｒ ,+,[,] )ｉｓａＬｉｅｒｉｎｇ ,ｃａｌｌｅｄｔｈｅａｓｓｏｃｉａｔｅｄＬｉｅｒｉｎｇｏｆＲ .ＩｔｗａｓｐｒｏｖｅｄｂｙＪｅｎｎｉｎｇｓ[1]ｔｈａｔ(Ｒ , )ｉｓａｎｉｌｐｏｔｅｎｔｇｒｏｕｐｉｆａｎｄｏｎｌｙｉｆ (…     

Abel π-正则环的扩张

本文研究了Abelπ-正则环的扩张.利用环的结构理论,证明了一个Abel环R(不必有1)是π-正则的当且仅当有理想I使得I和R/I都是π-正则的.推广了一些文献的结论.     

Rings with Maximal Finite Subrings

In[1 ] and[2 ] ,itwas proved thata ring with a finite maximal subring mustbe finite.Special cases of this result had been shown for commutative ring(see[3 ] ) and for PI-rings (see [4 ] ) . Lanski[5] extends the result to the ring with a finite maximal invariantsubring with respect to certain automorphism.In this paper,we shall consider ringswith maximal finite subrings. Such a ring,of course,is not necessarily finite. Becauseevery finite ring has maximal finite subrings,we shall be interest…     

The Structure of Almost Quasi-Regular Rings

Let R be a ring. It is well-known that R is a semigroup with respect to the composition a b=a b-ab for a,b∈R. An element a of R is said to be (right; left) quasi-regular if there exists an element b in R such that (a b=0;