On right GP-V-rings

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.