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Thursday, July 30, 2020 | History

4 edition of Almost completely decomposable groups found in the catalog.

Almost completely decomposable groups

by A. Mader

  • 284 Want to read
  • 30 Currently reading

Published by Gordon and Breach Science Publishers in Amsterdam, The Netherlands .
Written in English

    Subjects:
  • Abelian groups.,
  • Decomposition (Mathematics)

  • Edition Notes

    Includes bibliographical references (p. 343-346) and index.

    StatementAdolf Mader.
    SeriesAlgebra, logic, and applications ;, v. 13
    Classifications
    LC ClassificationsQA180 .M34 2000
    The Physical Object
    Paginationx, 354 p. ;
    Number of Pages354
    ID Numbers
    Open LibraryOL3630021M
    ISBN 109056992252
    LC Control Number2002421693
    OCLC/WorldCa41257172

    DeepDyve is the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Free shipping for non-business customers when ordering books at De Gruyter Online. Please find details to our shipping fees here. RRP: Recommended Retail Price. Print Flyer; Overview; Content; Previous chapter. Next chapter. Quotient divisible and almost completely decomposable groups Fomin, A. A. 30,00 € / $ / £ Get Access to.

    Kaplansky, in his "little red book", asserted that abelian group theory is really the study of modules over principal ideal domains, and since then most abelian group theorists tend to feel more at home with commutative ring theory than with group theory in general. Almost Completely Decomposable Modules Regulating Submodules 6. Splitting. In the work of Herden and Strüngmann (In Models, modules and Abelian groups () – de Gruyter), an embedding problem for torsion-free Abelian groups was considered. It was shown for a large class of such groups, including the class of all bounded extensions of completely decomposable groups, that any member of the class can be purely embedded into some completely decomposable group.

    The duals of almost completely decomposable groups, Archiv der Mathematik 68 (), The duals of Warfield groups, Pacific Journal of Mathematics (), Splitting of the identity component in locally compact abelian groups, Rendiconti del Seminario Matematico della Università di Padova 88 (), Block rigid almost completely decomposable groups and lattices over multiple pullback rings, J. Pure and Appl. Alg., 87 (), (with M. Dugas). Locally free finite rank Butler groups and near isomorphism, Abelian Groups and Modules, Kluwer, Boston, , 41 .


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Almost completely decomposable groups by A. Mader Download PDF EPUB FB2

An almost completely decomposable abelian (acd) group is an extension of a finite direct sum of subgroups of the additive group of rational numbers by a finite abelian group. Examples are easy to write and are frequently used but have been notoriously difficult to study and classify because of their computational nature.

However, a general theory of acd groups has been. Download Almost Completely Decomposable Groups books, An almost completely decomposable abelian (acd) group is an extension of a finite direct sum of subgroups of the additive group of rational numbers by a finite abelian group.

Examples are easy to write and are frequently used but have been notoriously difficult to study and classify because. An almost completely decomposable abelian (acd) group is an extension of a finite direct sum of subgroups of the additive group of rational numbers by a finite abelian group.

Examples are easy to write and are frequently used but have been notoriously difficult to study and classify because of their computational nature. However, a general Cited by: Book Almost completely decomposable groups book An almost completely decomposable abelian (acd) group is an extension of a finite direct sum of subgroups of the additive group of rational numbers by a finite abelian group.

Examples are easy to write and are frequently used but have been notoriously difficult to study and classify because of their computational nature. Notation and Background 2. Basics and Completely Decomposable Groups 3. Cyclic Essential Extensions 4.

Regulating Subgroups and Regulators 5. Local-Global Relationships 6. Groups with Cyclic Regulating 7. Completely Decomposable Summands 8. Anti-Representations 8. Near-Isomorphism and Type-Isomorphism 9. Fundamental Decomposition. Almost completely decomposable groups can be described in terms of integral matrices and in terms of anti-representations in finite modules over proper quotient rings of the ring of integers.

A completely decom — posable subgroup of an almost completely decomposable group of minimal index is called regulating subgroup by Lady [4]. The intersection of all regulating subgroups of A is the regulator R= R(A).

Burkhardt [2] proved, that the regulator is completely decomposable. Almost completely decomposable groups are torsion-free finite extensions of completely decomposable groups of finite rank.

We answer completely and in a constructive fashion the question when an. For almost completely decomposable groups, however, we do have the follow-ing weaker theorem: Theorem 6. If G is an almost completely decomposable group and G = A @ H = B @ K where A, B are r-homogeneous and H, K have no rank 1 summands of type r, then A ; B.

Proof. Note that A and B are necessarily completely decomposable groups. Almost completely decomposable torsion free abelian groups Proc. Amer. Math. Soc. 45(), pp. 41 - This was the first paper I ever wrote completely on my own. I started it during August,just after getting my degree at New Mexico State.

I finished it sometime before the end of the fall semester ALMOST COMPLETELY DECOMPOSABLE GROUPS A. MADĚR, O. MUTZBAUER AND C. VINSONHALER 1. Introduction. All groups in this paper are tacitly assumed to be abelian. An almost completely decomposable group is a torsion-free group of finite rank that contains a completely decomposable group as a subgroup of finite index.

Let X be such a group and. Almost completely decomposable groups We begin with the necessary definitions. A completely decomposable group (abelian is always assumed) is a torsion-free group that is isomorphic to a finite direct sum of subgroups of the additive rationals, st completely decomposable group is any torsion-free group that.

Features a stimulating selection of papers on abelian groups, commutative and noncommutative rings and their modules, and topological groups. Investigates currently popular topics such as Butler groups and almost completely decomposable groups.

Almost completely decomposable groups with a regulating regulator and a p-primary regulator quotient are is shown that there are indecomposable such groups of arbitrarily large rank provided that the critical typeset contains some basic configuration and the exponent of the regulator quotient is sufficiently large.

An almost completely decomposable group X is a finite essential abelian. extension of a completely decomposable group A of finite rank.

Almost completely decomposable groups appeared early in studies of torsion-free abelian groups, but only as examples, usually exhibiting pathological de-compositions. It presents the latest developments in the most active areas of abelian groups, particularly in torsion-free abelian groups.;For both researchers and graduate students, it reflects the current status of abelian group theory.;Abelian Groups discusses: finite rank Butler groups; almost completely decomposable groups; Butler groups of infinite.

For details on almost completely decomposable groups we refer to the book and for torsion-free abelian groups of finite rank in general to. Maximal completely decomposable summands of torsion-free abelian groups. An almost completely decomposable group is a torsion{free group of nite rank which contains a completely decomposable subgroup of nite index.

Lemma (Butler Decomposition) [Mad00, Lemma ] Let X be an almost completely decomposable group and ˝a critical type of X. Then X(˝) = A ˝ X](˝); and the Butler complement A ˝ is. Stanford Libraries' official online search tool for books, media, journals, databases, government documents and more.

Rings, modules, algebras and abelian groups: proceedings of the Algebra Conference--Venezia in SearchWorks catalog. Additives Galois Theory of Modules, 2. Finitely Generated and Cogenerated QD Groups, 3.

Direct Limits of Modules of Finite Projective Dimension. Classification of a Class of Almost Completely Decomposable Groups, 5. A Polynomial Ring Sampler, 6. The Picard Group of the Ring of Integer-valued Polynomials on a Valuation Domain, 7. 2 Almost completely decomposable groups Details on almost completely decomposable groups and representation of posets are found in [Mader00] and [Arnold00].

All “groups” in this paper are torsion-free abelian groups of finite rank. A completely decomposable subgroup Rof an almost completely decomposable group Gis.Project Euclid - mathematics and statistics online. R. Burkhardt, On a special class of almost completely decomposable groups I, in Abelian groups and modules, Proc.

of the Udine Conf.CISM Courses and Lectures, vol.Springer, Vienna,E. Blagoveshchenskaya, G. Ivanov and P. Schultz – The Baer-Kaplansky theorem for almost completely decomposable groups [MR ] Andreas Blass and John Irwin – Maximal pure independent sets [MR ] Dikran Dikranjan and Michael Tkachenko.