Self-Cancellation of Torsion-Free Abelian Groups of Finite Rank
Copyright policy )Self-Cancellation of Torsion-Free Abelian Groups of Finite Rank
An Abelian group \(A\) is said to have self-cancellation if \(A\oplus A\cong A\oplus B\) implies \(A\cong B\). A very simple example of a rank 4 torsion-free Abelian group without the self-cancellation property is constructed. The construction is based on the author's criterion [Algebra Anal. 7, No. 6, 33-78 (1995); corrections ibid. 11, No. 4, 222-224 (1999; Zbl 0861.16011)] for an Abelian group \(A\) to have self-cancellation in terms of certain properties of a maximal order in the semi-simple algebra \(\mathbb{Q} R\), where \(R=\mathbb{E}(A)/N(\mathbb{E}(A))\), \(\mathbb{E}(A)\) is the endomorphism ring of \(A\) and \(N(\mathbb{E}(A))\) is the nil-radical of \(\mathbb{E}(A)\).
Torsion-free groups, finite rank, Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Direct sums, direct products, etc. for abelian groups, maximal orders in semi-simple algebras, self-cancellation, torsion-free Abelian groups of finite rank
Torsion-free groups, finite rank, Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Direct sums, direct products, etc. for abelian groups, maximal orders in semi-simple algebras, self-cancellation, torsion-free Abelian groups of finite rank
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!