In this note we introduce a new ideal called subsemi-ideal of a ring R. We obtain a necessary and sufficient condition for a group ring to be a subsemi ideal ring.
The concept of derivations and generalized inner derivations has been generalized as an additive function δ： R → R satisfying δ （xy） = δ（x）y＋xd（y） for all x, y ∈ R, where d is a derivation on R. Such a fu...The concept of derivations and generalized inner derivations has been generalized as an additive function δ： R → R satisfying δ （xy） = δ（x）y＋xd（y） for all x, y ∈ R, where d is a derivation on R. Such a function δ is called a generalized derivation. Suppose that U is a Lie ideal of R such that u^2 ∈ U for all u ∈ U. In this paper, we prove that U lahtain in Z（R） when one of the following holds： （1） δ（[u, v]） = u o v =（2） δ（[u,v]）=[u o v] = 0 （3） δ（u o v） = [u, v] （4） δ（u o v）＋δ[u, v] = 0 for all u, v ∈ U.展开更多
文摘In this note we introduce a new ideal called subsemi-ideal of a ring R. We obtain a necessary and sufficient condition for a group ring to be a subsemi ideal ring.
文摘The concept of derivations and generalized inner derivations has been generalized as an additive function δ： R → R satisfying δ （xy） = δ（x）y＋xd（y） for all x, y ∈ R, where d is a derivation on R. Such a function δ is called a generalized derivation. Suppose that U is a Lie ideal of R such that u^2 ∈ U for all u ∈ U. In this paper, we prove that U lahtain in Z（R） when one of the following holds： （1） δ（[u, v]） = u o v =（2） δ（[u,v]）=[u o v] = 0 （3） δ（u o v） = [u, v] （4） δ（u o v）＋δ[u, v] = 0 for all u, v ∈ U.
