Let be a ring almost satisfying the descending chain condition for principal left ideals and has a unity. 本文主要研究了有单位元的主左理想几乎满足降链条件的环为完全环的条件。
Minimal condition extends DCC ( descending chain condition ) which is from finite to infinite. 极小条件是DCC(降链条件)从有限向无限的一种推广。
In the linear space with descending chain condition of subspaces, every subspace can be written as finite intersection of maxmin subspaces. 在满足子空间降链条件的线性空间中,每个子空间可表示为有限个极大子空间的交。
The following results are obtained : ( 1 ) If Ω is a right primitive ring, A is Ω non-nil ideal and left ideals of Ω contained in A practically satisfy the descending chain condition,Ω is a left primitive ring. 本文主要给出下述结果。(1)Ω为右本原环,A为Ω非零理想,Ω的真含于A的左理想几乎满足降链条件,则Ω也为左本原环。
Theorem 2 Let R be a subdirectly irreducible ring without any nonzero nilpotent element and the heart of R be H. If the left ideals of R contained in H satisfy the descending chain condition, then R is a division ring. 定理2设R为无非零幂零元的亚直不可约环,其心为H。若R的含于H的左理想具降链条件,则R为一体。