The balanced-projective dimension of Abelian p-groups. (English) Zbl 0602.20047

Fuchs, L.; Hill, P.

Trans. Am. Math. Soc. 293, 99-112 (1986).

A subgroup N of a p-primary abelian group M is isotype if \(p^{\alpha}M\cap N=p^{\alpha}N\) for all ordinals \(\alpha\), and it is nice if \((p^{\alpha}M+N)/N=p^{\alpha}(M/N)\) for all \(\alpha\). If N is both isotype and nice in M, it is said to be balanced in M, and the corresponding exact sequence \(0\to N\to M\to M/N\to 0\) is called balanced-exact. The category of balanced-exact sequences has enough projectives; these are the totally projective p-groups. The balanced- projective dimension of a p-group M is defined in the usual fashion, using balanced totally projective resolutions. The balanced-projective dimension of a p-group is determined by a structural property which generalizes Hill’s third axiom of countability.

Reviewer: K.Faltings

MSC:

20K10	Torsion groups, primary groups and generalized primary groups
20K27	Subgroups of abelian groups
20K40	Homological and categorical methods for abelian groups

Keywords:

isotype; nice; category of balanced-exact sequences; totally projective p-groups; balanced-projective dimension; balanced totally projective resolutions; Hill’s third axiom of countability