Descending Chain Condition

Views Updated: Dec 15, 2025

Key Facts

Abbreviation
DCC
Pronunciation
/dɪˈsɛndɪŋ ʧeɪn kənˈdɪʃən/
Category
Academic & Science
Related Field
Mathematics

Examples in Context

  1. Let be a ring almost satisfying the descending chain condition for principal left ideals and has a unity.
  2. Minimal condition extends DCC ( descending chain condition ) which is from finite to infinite.
  3. In the linear space with descending chain condition of subspaces, every subspace can be written as finite intersection of maxmin subspaces.
  4. 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.
  5. 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.

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