In this paper, we mainly study the structural notions of Frattini subalgebra and Jacobson radical of n-Lie algebras. The properties on Frattini subalgebra and the relationship between the Frattini subalgebra and Jacob...In this paper, we mainly study the structural notions of Frattini subalgebra and Jacobson radical of n-Lie algebras. The properties on Frattini subalgebra and the relationship between the Frattini subalgebra and Jacobson radical are studied. Moreover, we also study them when an n-Lie algebra is strong semi-simple, k-solvable and nilpotent.展开更多
在条件ab=φ(ba)下,研究了ab与a+b的伪Drazin逆的表达式.其中,a,b是Banach代数A中的2个伪Drazin可逆的元素,φ是A上双射的centralizer.证明了:若a,b是伪Drazin可逆的且ab=φ(ba),则ab是伪Drazin可逆的且(ab)~=b~a~;a+b是伪Drazin...在条件ab=φ(ba)下,研究了ab与a+b的伪Drazin逆的表达式.其中,a,b是Banach代数A中的2个伪Drazin可逆的元素,φ是A上双射的centralizer.证明了:若a,b是伪Drazin可逆的且ab=φ(ba),则ab是伪Drazin可逆的且(ab)~=b~a~;a+b是伪Drazin可逆的,当且仅当aa~(a+b)是伪Drazin可逆的,当且仅当aa~(a+b)bb~是伪Drazin可逆的.此时,(a+b)~=(aa~(a+b))~+sum from n=0 to ∞φ-(n(n+1))/2(1)(b~)^(n+1)(-a)~n(1-aa~).展开更多
Let R be a ring and a an automorphism of R. Amitsur proved that the Jacobson radical J（R[x]） of the polynomial ring R[x] is the polynomial ring over the nil ideal J（R[x]）∩R. Following Amitsur, it is shown that wh...Let R be a ring and a an automorphism of R. Amitsur proved that the Jacobson radical J（R[x]） of the polynomial ring R[x] is the polynomial ring over the nil ideal J（R[x]）∩R. Following Amitsur, it is shown that when R is an Armendaxiz ring of skew inverse Laurent series type and S is any one of the ring extensions R[x; α], R[x,x^-1;α], R[[x^-1;α]] and R（（x^-1; α））, then （S） = （R）S = Nil（S）, （S） ∩ R = Nil（R）, where is a radical in a class of radicals which includes the Wedderburn, lower nil, Levitzky and upper nil radicals.展开更多
基金Supported by the NSF (10270176) of Chinathe NSF (y2004034) of Hebei Universitythe NSF (2005000088) of Hebei Province,P.R.China
文摘In this paper, we mainly study the structural notions of Frattini subalgebra and Jacobson radical of n-Lie algebras. The properties on Frattini subalgebra and the relationship between the Frattini subalgebra and Jacobson radical are studied. Moreover, we also study them when an n-Lie algebra is strong semi-simple, k-solvable and nilpotent.
文摘在条件ab=φ(ba)下,研究了ab与a+b的伪Drazin逆的表达式.其中,a,b是Banach代数A中的2个伪Drazin可逆的元素,φ是A上双射的centralizer.证明了:若a,b是伪Drazin可逆的且ab=φ(ba),则ab是伪Drazin可逆的且(ab)~=b~a~;a+b是伪Drazin可逆的,当且仅当aa~(a+b)是伪Drazin可逆的,当且仅当aa~(a+b)bb~是伪Drazin可逆的.此时,(a+b)~=(aa~(a+b))~+sum from n=0 to ∞φ-(n(n+1))/2(1)(b~)^(n+1)(-a)~n(1-aa~).
文摘Let R be a ring and a an automorphism of R. Amitsur proved that the Jacobson radical J（R[x]） of the polynomial ring R[x] is the polynomial ring over the nil ideal J（R[x]）∩R. Following Amitsur, it is shown that when R is an Armendaxiz ring of skew inverse Laurent series type and S is any one of the ring extensions R[x; α], R[x,x^-1;α], R[[x^-1;α]] and R（（x^-1; α））, then （S） = （R）S = Nil（S）, （S） ∩ R = Nil（R）, where is a radical in a class of radicals which includes the Wedderburn, lower nil, Levitzky and upper nil radicals.
