Results 1 to 10 of about 158 (111)
Rings on Abelian torsion-free groups of finite rank [PDF]
Beitrage Zur Algebra Und Geometrie, 2021 In the class of reduced Abelian torsion-free groups $G$ of finite rank, we describe TI-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.
E I Kompantseva +2 more
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Summands of finite rank torsion free abelian groups
Journal of Algebra, 1974 AbstractA finite rank torsion free abelian group has, up to isomorphism, only finitely many summands.
E L Lady
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Multiplication Groups of Abelian Torsion-Free Groups of Finite Rank
Mediterranean Journal of Mathematics, 2023 For an Abelian group $G$, any homomorphism $μ\colon G\otimes G\rightarrow G$ is called a \textsf{multiplication} on $G$. The set $\text{Mult}\,G$ of all multiplications on an Abelian group $G$ itself is an Abelian group with respect to addition; the group is called the \textsf{multiplication group} of $G$.
E. I. Kompantseva, A. A. Tuganbaev
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Hypertypes of torsion-free abelian groups of finite rank [PDF]
Bulletin of the Australian Mathematical Society, 1989 Let G be a torsion-free abelian group of finite rank n and let F be a full free subgroup of G. Then G/F is isomorphic to T1 ⊕ … ⊕ Tn, where T1 ⊆ T2 ⊆ … ⊆ Tn ⊆ ℚ/ℤ. It is well known that type T1 = inner type G and type Tn = outer type G. In this note we give two characterisations of type Ti for 1 < i < n.
Goeters, H. P. +2 more
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A note on torsion-free abelian groups of finite rank [PDF]
Proceedings of the American Mathematical Society, 1973 Let G be a torsion-free abelian group of rank n and X= {xl, *. , x,j a maximal set of rationally independent elements in G. It is well known that any g e G can be uniquely written g= oc1xl?+ +x, for some cci, . , ?C72, E Q, the rational numbers. This enables us to define, for any such (G, X), a collection of subgroups of Q and "natural" isomorphisms ...
Wickless, W., Vinsonhaler, C.
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Structure of Finite-Dimensional Protori
Axioms, 2019 A Structure Theorem for Protori is derived for the category of finite-dimensional protori (compact connected abelian groups), which details the interplay between the properties of density, discreteness, torsion, and divisibility within a finite ...
Wayne Lewis
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Discussiones Mathematicae - General Algebra and Applications, 2017 It is studied how rank two pure subgroups of a torsion-free Abelian group of rank three influences its structure and type set. In particular, the criterion for such a subgroup B to be a direct summand of a torsion-free Abelian group of rank three with ...
Najafizadeh Alireza, Woronowicz Mateusz
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A Cancellation Criterion for Finite-Rank Torsion-Free Abelian Groups [PDF]
Proceedings of the American Mathematical Society, 1985 In this paper, a necessary ring-theoretical criterion is given for a finite-rank torsion-free abelian group to have the cancellation property. This generalizes results obtained by L. Fuchs and F. Loonstra [ 5 ] for the rank-one case and resolves the cancellation problem for strongly ...
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On decomposable pseudofree groups
International Journal of Mathematics and Mathematical Sciences, 1999 An Abelian group is pseudofree of rank ℓ if it belongs to the extended genus of ℤℓ, i.e., its localization at every prime p is isomorphic to ℤpℓ.
Dirk Scevenels
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Groups with minimax commutator subgroup [PDF]
International Journal of Group Theory, 2014 A result of Dixon, Evans and Smith shows that if $G$ is a locally (soluble-by-finite) group whose proper subgroups are (finite rank)-by-abelian, then $G$ itself has this property, i.e. the commutator subgroup of~$G$ has finite rank.
Francesco de Giovanni, Trombetti
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