For a ring R, let ip（RR）={a ∈ R： every right R-homomorphism f from any right ideal of R into R with Imf = aR can extend to R}. It is known that R is right IP-injective if and only if R = ip（RR） and R is right si...For a ring R, let ip（RR）={a ∈ R： every right R-homomorphism f from any right ideal of R into R with Imf = aR can extend to R}. It is known that R is right IP-injective if and only if R = ip（RR） and R is right simple-injective if and only if {a ∈ R ： aR is simple} ∪→ ip（RR）. In this note, we introduce the concept of right S-IP-injective rings, i.e., the ring R with S ∪→ ip（RR）, where S is a subset of R. Some properties of this kind of rings are obtained.展开更多
基金the Specialized Research Fund for the Doctoral Program of Higher Education of China (20020284009, 20030284033)the Postdoctoral Research Fund of China (2005037713)Jiangsu Planned Projects for Postdoctoral Research Fund (0203003403)
文摘For a ring R, let ip（RR）={a ∈ R： every right R-homomorphism f from any right ideal of R into R with Imf = aR can extend to R}. It is known that R is right IP-injective if and only if R = ip（RR） and R is right simple-injective if and only if {a ∈ R ： aR is simple} ∪→ ip（RR）. In this note, we introduce the concept of right S-IP-injective rings, i.e., the ring R with S ∪→ ip（RR）, where S is a subset of R. Some properties of this kind of rings are obtained.
