The maximal ideal is the only isolated subgroup of \ mathbb Z.
2.
The set of isolated subgroups is totally ordered by inclusion.
3.
Under this correspondence, the nonzero prime ideals of " D " correspond bijectively to the isolated subgroups of ?.
4.
A subgroup of ? is called an " isolated subgroup " if it is a segment and is a proper subgroup.
5.
Since the nonzero prime ideals are totally ordered and they correspond to isolated subgroups of ?, the height of ? is equal to the Krull dimension of the valuation ring " D " associated with ?.
6.
"Homo habilis " has often been thought to be the ancestor of the more cladogenetic rather than anagenetic ( meaning that if an isolated subgroup population of " H . habilis " became the ancestor of " H . erectus ", other subgroups remained as unchanged " H . habilis " until their much later extinction ).
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