Torsion-free rings

Kompantseva, E. I.

doi:10.1007/s10958-010-0132-6

Cited by 11 publications

(7 citation statements)

References 3 publications

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“…where P 1 ⊆ P, G p is the p-adic completion of the group G, e p ∈ G p . According to [19], the ring ( G, ×) is the direct product of ideals Z p e p , p ∈ P 1 . In addition, if e p × e p = τ p e p , where τ p ∈ Z p , then αe p × βe p = (αβτ p )e p for all p ∈ P 1 and α, β ∈ Z p .…”

Section: Every Homogeneous Murley Group Is Strongly Indecomposablementioning

confidence: 99%

Rings on Abelian Torsion-Free Groups of Finite Rank

Kompantseva¹,

Tuganbaev²

2021

Preprint

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In the class of reduced Abelian torsion-free groups G of finite rank, we describe T I-groups, this means that every associative ring on G is filial. If every associative multiplication on G is the zero multiplication, then G is called a nil a -group. It is proved that a reduced Abelian torsionfree group G of finite rank is a T I-group if and only if G is a homogeneous Murley group or G is a nil a -group. We also study the interrelations between the class of homogeneous Murley groups and the class of nil a -groups. For any type t = (∞, ∞, . . .) и every integer n > 1, there exist 2 ℵ 0 pairwise nonquasi-isomorphic homogeneous Murley groups of type t and rank n which are nil a -groups. We describe types t such that there exists a homogeneous Murley group of type t which is not a nil a -group. This paper will be published in Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry.

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Section: Every Homogeneous Murley Group Is Strongly Indecomposablementioning

confidence: 99%

Rings on Abelian Torsion-Free Groups of Finite Rank

Kompantseva¹,

Tuganbaev²

2021

Preprint

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“…It is known from [6] that the following equalities hold for the reduced algebraically compact group A and divisible torsion group D:…”

Section: Theorem 5 If G Is a Cotorsion Group That Contains No Nonzermentioning

confidence: 99%

“…Since the absolute radical of a direct sum of subgroups is contained in the direct sum of their absolute radicals [6], from (1)-(3) and Proposition 2 we have…”

Section: Theorem 5 If G Is a Cotorsion Group That Contains No Nonzermentioning

confidence: 99%

Abelian dqt-Groups and Rings on Them

Kompantseva

2015

J Math Sci

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“…For an Abelian group G, a multiplication on G is a homomorphism µ : G⊗G → G. The set Mult G of all multiplications on the group G itself is an Abelian group with respect to addition; the group is called the multiplication group of G or the group of multiplications on G [9]. An Abelian group G with multiplication on G is called a ring on the group G. The problem of studying the relationship between the structure of an Abelian group and the properties of ring structures on it is very multifaceted and has a long history in algebra; see [1], [2], [6], [7], [10], [11], [13], [14].…”

Section: Introductionmentioning

confidence: 99%

Multiplication Groups of Abelian Torsion-Free Groups of Finite Rank

Kompantseva¹,

Tuganbaev²

2022

Preprint

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For an Abelian group G, any homomorphism µ : G ⊗ G → G is called a multiplication on G. The set Mult G of all multiplications on an Abelian group G itself is an Abelian group with respect to addition; the group is called the multiplication group of G. Let A 0 be the class of all reduced block-rigid almost completely decomposable groups of ring type with cyclic regulator quotient. In this paper, for groups G ∈ A 0 , we describe groups Mult G. We prove that for G ∈ A 0 , the group Mult G also belongs to the class A 0 . For any group G ∈ A 0 , we describe the rank, the regulator, the regulator index, invariants of near-isomorphism, a main decomposition, and a standard representation of the group Mult G.

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Torsion-free rings

Cited by 11 publications

References 3 publications

Rings on Abelian Torsion-Free Groups of Finite Rank

Rings on Abelian Torsion-Free Groups of Finite Rank

Abelian dqt-Groups and Rings on Them

Multiplication Groups of Abelian Torsion-Free Groups of Finite Rank

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