Results 11 to 20 of about 39,179 (265)
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. Lady
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Splitting mixed groups of torsion-free finite rank II
Hokkaido Mathematical Journal, 2013 First we introduce the concept of QD-hulls in arbitrary abelian groups. Then we use the concept to give a new characterization of purifiable torsion-free finite rank subgroups of an arbitrary abelian group. Finally we use it to formulate a splitting criterion for mixed groups of torsion-free finite rank.
T. Okuyama
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On the structure of groups admitting faithful modules with certain conditions of primitivity
Researches in Mathematics, 2023 In the paper we study structure of soluble-by-finite groups of finite torsion-free rank which admit faithful modules with conditions of primitivity. In particular, we prove that under some additional conditions if an infinite finitely generated linear ...
A.V. Tushev
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The Grothendieck and Picard groups of finite rank torsion free $$\mathfrak {sl}(2)$$-modules
RACSAM, 2022 The classification problem for simple $${\mathfrak {sl}(2)}$$ sl ( 2 ) -modules leads in a natural way to the study of the category of finite rank torsion free $${\mathfrak {sl}(2)}$$ sl ( 2 ) -modules and its subcategory of rational $${
F. J. Plaza Martín, C. Tejero Prieto
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Centrally essential torsion-free rings of finite rank [PDF]
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2020 It is proved that centrally essential rings, whose additive groups of finite rank are torsion-free groups of finite rank, are quasi-invariant but not necessarily invariant.
O. Lyubimtsev, 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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Completely decomposable direct summands of torsion-free abelian groups of finite rank [PDF]
, 2017 Let $A$ be a finite rank torsion--free abelian group. Then there exist direct decompositions $A=B\oplus C$ where $B$ is completely decomposable and $C$ has no rank 1 direct summand.
A. Mader, P. Schultz
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On the Classification Problem for Rank 2 Torsion-Free Abelian Groups [PDF]
, 2000 We study here some foundational aspects of the classification problem for torsion-free abelian groups of finite rank. These are, up to isomorphism, the subgroups of the additive groups (Q^n, +), for some n = 1, 2, 3,....
Kechris, Alexander S.
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