半素PI-环的本质(单边)理想

The Essential(One-Sided) Ideals of Semiprime PI-Rings

本文系统研究了半素ＰＩ－环本质（单边）理想及最大商环的有关性质，从ＰＩ－理论中著名的 Ｒｏｗｅｎ非平凡相交定理出发，证明了半素 ＰＩ－环的本质（单边）理想包合一个本质两边理想（定理７，推论８），建立了半素ＰＩ－环本质（单边）理想与其中心本质理想的内在联系（定理 ９，推论 １０），并以此为基础，证明了半素 ＰＩ－环的最大商环是 ＰＩ的（定理 １２），且半素 ＰＩ－环的每一正则元在其最大商环中是可逆的（定理 １４）．

We research some properties on the essential (one-sided) ideals and the maximal quotient rings of smiprime PI-rings. The main resu is proved in this paper are that if R is a semiprine PI-rings then every essential one-sided ideal of R contains an essential two-sided ideal of R (Th7, Cor8), the connection between essential one sided ideals of R and essential ideals of the center are indicated (Th9 Cor10), the maximal quotient ring of R is also PI (Th12), every regular element in R is invertible in maximal quotient ring (Th14).