数学研究与评论
數學研究與評論
수학연구여평론
JOURNAL OF MATHEMATICAL RESEARCH AND EXPOSITION
2006年
1期
27-32
,共6页
S-IP-内射环%单-内射环%C2-环
S-IP-內射環%單-內射環%C2-環
S-IP-내사배%단-내사배%C2-배
S-IP-injective ring%simple-injective ring%C2-ring
对环R,令ip(RR)={a∈R:任意一个从R的右理想到R且象为aR的模同态能开拓到R}.众所周知,R为右IP-内射环当且仅当R=ip(RR),R为右单-内射环当且仅当{a∈R:aR is simple}( )ip(RR).对环R的一个子集S,我们引进了S-IP-内射环的概念,即满足S( )ip(RR)的环.并得到了这种环的一些性质.
對環R,令ip(RR)={a∈R:任意一箇從R的右理想到R且象為aR的模同態能開拓到R}.衆所週知,R為右IP-內射環噹且僅噹R=ip(RR),R為右單-內射環噹且僅噹{a∈R:aR is simple}( )ip(RR).對環R的一箇子集S,我們引進瞭S-IP-內射環的概唸,即滿足S( )ip(RR)的環.併得到瞭這種環的一些性質.
대배R,령ip(RR)={a∈R:임의일개종R적우이상도R차상위aR적모동태능개탁도R}.음소주지,R위우IP-내사배당차부당R=ip(RR),R위우단-내사배당차부당{a∈R:aR is simple}( )ip(RR).대배R적일개자집S,아문인진료S-IP-내사배적개념,즉만족S( )ip(RR)적배.병득도료저충배적일사성질.
For a ring R, let ip(RR) = {a ∈ R: every rightR-homomorphism f from any right ideal ofR into R with Imf = aR can extend to R}. It is known thatR 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.
