Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The balanced-projective dimension of abelian $ p$-groups

Authors: L. Fuchs and P. Hill
Journal: Trans. Amer. Math. Soc. 293 (1986), 99-112
MSC: Primary 20K10; Secondary 20K27
MathSciNet review: 814915
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The balanced-projective dimension of every abelian $ p$-group is determined by means of a structural property that generalizes the third axiom of countability. As a corollary to our general structure theorem, we show for $ \lambda = {\omega _n}$ that every $ {p^\lambda }$-high subgroup of a $ p$-group $ G$ has balanced-projective dimension exactly $ n$ whenever $ G$ has cardinality $ {\aleph _n}$ but $ {p^\lambda }G \ne 0$. Our characterization of balanced-projective dimension also leads to new classes of groups where different infinite dimensions are distinguished.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 20K10, 20K27

Retrieve articles in all journals with MSC: 20K10, 20K27

Additional Information

Keywords: Balanced-projective dimension, Axiom 3, totally projective, separable subgroups, balanced submodules, continuous chain, Auslander's lemma, valuated $ p$-groups
Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society