Subgroups of the Baer–Specker group with few endomorphisms but large dual

• Autorzy: Andreas Blass , Rüdiger Göbel
• Języki publikacji: EN

Abstrakty

EN

Assuming the continuum hypothesis, we construct a pure subgroup G of the Baer-Specker group $ℤ^{ℵ_0}$ with the following properties. Every endomorphism of G differs from a scalar multiplication by an endomorphism of finite rank. Yet G has uncountably many homomorphisms to ℤ.

Kategorie tematyczne

• 03E50: Continuum hypothesis and Martin's axiom
• 20K30: Automorphisms, homomorphisms, endomorphisms, etc.
• 20K25: Direct sums, direct products, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1996
• Tom: 149
• Numer: 1
• Strony: 19-29

Daty

wydano

1996

otrzymano

1994-03-25

poprawiono

1995-10-05

Twórcy

autor

Andreas Blass

• Mathematics Department, University of Michigan, Ann Arbor, Michigan 48109, U.S.A.

autor

Rüdiger Göbel

• Fachbereich 6, Mathematik, Universität Essen, 45117 Essen, Germany

Bibliografia

• [1] A. Blass, Cardinal characteristics and the product of countably many infinite cyclic groups, J. Algebra 169 (1994), 512-540.
• [2] A. Blass, Near coherence of filters, II: Applications to operator ideals, the Stone-Čech remainder of a half-line, order ideals of sequences, and slenderness of groups, Trans. Amer. Math. Soc. 300 (1987), 557-581.
• [3] A. Blass and C. Laflamme, Consistency results about filters and the number of inequivalent growth types, J. Symbolic Logic 54 (1989), 50-56.
• [4] S. U. Chase, Function topologies on abelian groups, Illinois J. Math. 7 (1963), 593-608.
• [5] A. L. S. Corner, A class of pure subgroups of the Baer-Specker group, unpublished talk given at Montpellier Conference on Abelian Groups, 1967.
• [6] A. L. S. Corner and R. Göbel, Prescribing endomorphism algebras, a unified treatment, Proc. London Math. Soc. 50 (1985), 447-479.
• [7] A. L. S. Corner and B. Goldsmith, On endomorphisms and automorphisms of some pure subgroups of the Baer-Specker group, in: Abelian Group Theory and Related Topics, R. Göbel, P. Hill and W. Liebert (eds.), Contemp. Math. 171, 1994, 69-78.
• [8] M. Dugas und R. Göbel, Die Struktur kartesischer Produkte der ganzen Zahlen modulo kartesische Produkte ganzer Zahlen, Math. Z. 168 (1979), 15-21.
• [9] M. Dugas und R. Göbel, Endomorphism rings of separable torsion-free abelian groups, Houston J. Math 11 (1985), 471-483.
• [10] M. Dugas and J. Irwin, On basic subgroups of Π Z, Comm. Algebra 19 (1991), 2907-2921.
• [11] M. Dugas and J. Irwin, On pure subgroups of cartesian products of integers, Resultate Math. 15 (1989), 35-52.
• [12] M. Dugas, J. Irwin and S. Khabbaz, Countable rings as endomorphism rings, Quart. J. Math. Oxford 39 (1988), 201-211.
• [13] K. Eda, A note on subgroups of $ℤ^ℕ$, in: Abelian Group Theory, R. Göbel, L. Lady and A. Mader (eds.), Lecture Notes in Math. 1006, Springer, 1983, 371-374.