摘要
利用星型算子理论的相关方法,对Krull整环与π-整环进行了研究,给出了π-整环上形式幂级数的一些容度准则,证明了整环R是π-整环当且仅当对f,g∈R[[X]]*,都■h∈K[X]*,使得c(f)w=c(g)wc(h)w;当且仅当对f,g∈R[[X]]*,都■h∈K[X]*,使得c(f)t=c(g)tc(h)t;当且仅当对f∈R[X]*,g∈R[[X]]*,都■h∈K[X]*,使得c(f)w=c(g)wc(h)w;当且仅当对f∈R[X]*,g∈R[[X]]*,都■h∈K[X]*,使得c(f)t=c(g)tc(h)t.
By utilizing the relevant methods of star operation theory, we study Krull domains and π-πdomains, and show some con- tent formulas for power series over π-domains. It is proved that an integral domain R is a π-πdomain if and only if for any f,g∈ R[[X] ] , there exists h ∈K[X] such that c(f) w = c(g)w c(h)w, if and only if for any f,g ∈ R[ [ X] ], there exists h ∈ K[X] such thatc(f),=c(g),c(h),, if and only if for anyf∈R[X],g∈R[[X]], there exists h∈K[X] such that c(f)w = c(g) wc(h) w, if and only if for anyf∈ R[ X] ,g ∈ R[ [X]], there exists h ∈K[ X] such that c(f)t = c(g)tc(h)t.
出处
《四川师范大学学报(自然科学版)》
CAS
CSCD
北大核心
2014年第4期451-454,共4页
Journal of Sichuan Normal University(Natural Science)
基金
国家自然科学基金(11171240)
教育部博士点基金(20125134110002)
四川省教育厅自然科学重点基金(14ZB0035)资助项目