摘要
主要研究GP-V-环(GP—V-模),它是P—V-环(P—V-模)的推广.讨论了这一类环的某些性质,例如:设R是GP—V-环,则对主右理想U=αR的任意极大子理想K,存在n∈Z^+和R的极大右理想H使得H∩α^nR=K∩α^nR;右GP—V-环的每个主右理想都是幂等的;右GP—V-环的直和项仍是右GP—V-环;等等.此外,还讨论了右GP—V-环什么时候是Von Neumann正则环.
GP-V-ring(GP-V-module) is studied which is a generalization of P-V-ring (P-V-module), and the characters are searched for. For example, if R is a right GP-V-ring, then for any maximal subideal K of a principal right ideal U= αR,α∈ R, there exists a maximal right ideal H of R that H ∩ α^nR =K ∩ α^nR, for some n ∈ Z^+ Every principal right ideal of a right GP-V-ring is idempotent, any direct summand of a right GP-V-ring is again a right GP-V- ring and so on. Furthermore, the question when a GP-V-ring is Von Neumann regular is discussed in the remainder.
出处
《浙江大学学报(理学版)》
CAS
CSCD
北大核心
2009年第3期249-253,共5页
Journal of Zhejiang University(Science Edition)