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Smooth invariants and ω -graded modules over k [ X ]

Fred Richman (2000)

Commentationes Mathematicae Universitatis Carolinae

It is shown that every ω -graded module over k [ X ] is a direct sum of cyclics. The invariants for such modules are exactly the smooth invariants of valuated abelian p -groups.

Some generalizations of torsion-free Crawley groups

Brendan Goldsmith, Fatemeh Karimi, Ahad Mehdizadeh Aghdam (2013)

Czechoslovak Mathematical Journal

In this paper we investigate two new classes of torsion-free Abelian groups which arise in a natural way from the notion of a torsion-free Crawley group. A group G is said to be an Erdős group if for any pair of isomorphic pure subgroups H , K with G / H G / K , there is an automorphism of G mapping H onto K ; it is said to be a weak Crawley group if for any pair H , K of isomorphic dense maximal pure subgroups, there is an automorphism mapping H onto K . We show that these classes are extensive and pay attention to...

The generalized criterion of Dieudonné for valuated p -groups

Peter Vassilev Danchev (2006)

Acta Mathematica Universitatis Ostraviensis

We prove that if G is an abelian p -group with a nice subgroup A so that G / A is a Σ -group, then G is a Σ -group if and only if A is a Σ -subgroup in G provided that A is equipped with a valuation induced by the restricted height function on G . In particular, if in addition A is pure in G , G is a Σ -group precisely when A is a Σ -group. This extends the classical Dieudonné criterion (Portugal. Math., 1952) as well as it supplies our recent results in (Arch. Math. Brno, 2005), (Bull. Math. Soc. Sc. Math....

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