Quotient divisible abelian groups

Authors:
A. Fomin and W. Wickless

Journal:
Proc. Amer. Math. Soc. **126** (1998), 45-52

MSC (1991):
Primary 20K21, 20K40

DOI:
https://doi.org/10.1090/S0002-9939-98-04230-0

MathSciNet review:
1443826

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: An abelian group is called quotient divisible if is of finite torsion-free rank and there exists a free subgroup such that is divisible. The class of quotient divisible groups contains the torsion-free finite rank quotient divisible groups introduced by Beaumont and Pierce and essentially contains the class of self-small mixed groups which has recently been investigated by several authors. We construct a duality from the category of quotient divisible groups and quasi-homomorphisms to the category of torsion-free finite rank groups and quasi-homomorphisms. Our duality when restricted to torsion-free quotient divisible groups coincides with the duality of Arnold and when restricted to coincides with the duality previously constructed by the authors.

**[A]**D. Arnold, A duality for quotient divisible abelian groups of finite rank, Pac. J. Math. 42 (1972), 11-15. MR**47:361****[AGW]**U. Albrecht, H.P. Goeters and W. Wickless, The flat dimension of mixed abelian groups as E-modules, Rocky Mt. J. Math. 25(2) (1995), 569-90. MR**96f:20086****[BP]**R. Beaumont and R. Pierce, Torsion-free rings, Ill. J. Math. 5 (1961), 61-98. MR**26:6212****[FiW]**S. Files and W. Wickless, The Baer-Kaplansky Theorem for a class of global mixed abelian groups, Rocky Mt. J. Math. 26(2) (1996), 593-613. CMP**96:17****[Fo1]**A. Fomin, The category of quasi-homomorphisms of abelian torsion-free groups of finite rank, Cont. Math. 131 (1992), 91-111. MR**93j:20108****[Fo2]**-, Finitely presented modules over the ring of universal numbers, Cont. Math. 171 (1994), 109-120. MR**95i:20074****[FoW]**A. Fomin and W. Wickless, Categories of mixed and torsion-free abelian groups, Abelian Groups and Modules, Kluwer, Boston, 1995, 185-92. MR**97c:20083****[Fu]**L. Fuchs, Infinite Abelian Groups I, II, Academic Press, New York, 1970, 1973. MR**41:333**; MR**50:2362****[GW]**S. Glaz and W. Wickless, Regular and principal projective endomorphism rings of mixed abelian groups, Comm. in Algebra 22(4) (1994), 1161-76. MR**95a:20060****[VW]**C. Vinsonhaler and W. Wickless, Realizations of finite dimensional algebras over the rationals, Rocky Mt. J. Math.24(4) (1994), 1553-65. MR**96e:20089****[Wi]**W. Wickless, A functor from mixed groups to torsion-free groups, Cont. Math. 171 (1995), 407-19. MR**95k:20090**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
20K21,
20K40

Retrieve articles in all journals with MSC (1991): 20K21, 20K40

Additional Information

**A. Fomin**

Affiliation:
Algebra Department, Moscow State Pedagogical University, Moscow, Russia

Email:
fomin.algebra@mpgu.msk.su

**W. Wickless**

Affiliation:
Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269

Email:
wjwick@uconnvm.uconn.edu

DOI:
https://doi.org/10.1090/S0002-9939-98-04230-0

Received by editor(s):
June 14, 1996

Dedicated:
Dedicated to the memory of Ross A. Beaumont

Communicated by:
Ronald M. Solomon

Article copyright:
© Copyright 1998
American Mathematical Society