ascending chain condition sentence in Hindi

Examples

1. The Artin Wedderburn theorem generalises this result, with the ascending chain condition.
2. In this case " R " is also said to satisfy the ascending chain condition.
3. An integral domain that satisfies the ascending chain conditions on divisorial ideals is called a Mori domain.
4. The same equivalence holds for infinite lattices which satisfy the ascending chain condition ( or the descending chain condition ).
5. A more algebraic way to see this is that the associated ideals defining algebraic sets must satisfy the ascending chain condition.
6. Although the descending chain condition appears dual to the ascending chain condition, in rings it is in fact the stronger condition.
7. The lattice of subgroups of a group satisfies the ascending chain condition if and only if all subgroups of the group are finitely generated.
8. A collection of subsets of a given set satisfies the ascending chain condition if any ascending sequence becomes constant after a finite number of steps.
9. Note that graded posets need not satisfy the ascending chain condition ( ACC ) : for instance, the natural numbers contain the infinite ascending chain 0.
10. A Noetherian module is a module which satisfies the ascending chain condition on submodules, that is, every increasing chain of submodules becomes stationary after finitely many steps.