Direct sums ofJ-rings and radical rings
1995 ◽
Vol 18
(3)
◽
pp. 531-534
LetRbe a ring,J(R)the Jacobson radical ofRandPthe set of potent elements ofR. We prove that ifRsatisfies(∗)givenx,yinRthere exist integersm=m(x,y)>1andn=n(x,y)>1such thatxmy=xynand if eachx∈Ris the sum of a potent element and a nilpotent element, thenNandPare ideals andR=N⊕P. We also prove that ifRsatisfies(∗)and if eachx∈Rhas a representation in the formx=a+u, wherea∈Pandu∈J(R),thenPis an ideal andR=J(R)⊕P.
2005 ◽
Vol 2005
(9)
◽
pp. 1387-1391
2013 ◽
Vol 12
(05)
◽
pp. 1250208
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2008 ◽
Vol 2008
◽
pp. 1-6
1991 ◽
Vol 34
(2)
◽
pp. 260-264
◽
2012 ◽
Vol 2012
(1)
◽
pp. 7
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Keyword(s):
2012 ◽
Vol 262
(5)
◽
pp. 2013-2030
◽
1979 ◽
Vol 23
◽
pp. 275-280
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Keyword(s):