Torsion-free abelian group

About: Torsion-free abelian group is a research topic. Over the lifetime, 71 publications have been published within this topic receiving 3099 citations.

Direct sums of local torsion-free abelian groups

Abstract: The category of local torsion-free abelian groups of finite rank is known to have the cancellation and n-th root properties but not the Krull-Schmidt property. It is shown that 10 is the least rank of a local torsion-free abelian group with two non-equivalent direct sum decompositions into indecomposable summands. This answers a question posed by M.C.R. Butler in the 1960's.

Jordan tori for a torsion free abelian group

Abstract: We classify Jordan G-tori, where G is any torsion-free abelian group Using the Zelmanov prime structure theorem, such a class divides into three types, the Hermitian type, the Clifford type, and the Albert type We concretely describe Jordan G-tori of each type

Stacked bases for a pair of homogeneous completely decomposable groups with bounded quotient

Abstract: Let A be a homogeneous completely decomposable torsion free group of infinite rank κ and let X be a torsion free abelian group containing A such that the quotient X/A is bounded We show that there exist stacked bases for X and A, ie there exist b i ∈ X (i ∈ κ) and d i ∈ ℤ (i ∈ κ) such that \( X = \mathop \oplus \limits_{i \in k} \left\langle {{b_i}} \right\rangle _*^X \) and \( A = \mathop \oplus \limits_{i \in k} {d_i}\left\langle {{b_i}} \right\rangle _*^A \) This proves a stacked bases theorem for pairs of homogeneous completely decomposable torsion free abelian groups of infinite rank with bounded quotient