A-Whitehead groups
Keywords:
Whitehead modules, endomorphism rings, adjoint functors.Abstract
This paper investigates various extensions of the notion of Whitehead modules. An Abelian group G is an A-Whitehead group if there exists an exact sequence 0 ! U ! _IA ! G ! 0 such that SA(U) = U with respect to which A is injective. We investigate the structure of A-Whitehead groups.
Mathematics Subject Classification (2010): 20K20, 20K40.
References
Albrecht, U., Endomorphism Rings and A-Projective Torsion-Free Abelian Groups, Abelian Group Theory, Proceedings Honolulu 1982/83, Springer Lecture Notes in Mathematics 1006, Springer Verlag, Berlin, New York, Heidelberg, 1983, 209-227.
Albrecht, U., Baer's Lemma and Fuchs' Problem 84a, Transactions of the American Mathematical Society, 293(1986), 565-582.
Albrecht, U., Extension Functors on the Category of A-Solvable Abelian Groups, Czechoslovak Journal of Mathematics, 41(116)(1991), 685-694.
Albrecht, U., Endomorphism Rings, Tensor products, and Fuchs' Problem 47, Warfield Memorial Volume; Contemporary Mathematics, 130(1992), 17-31.
Albrecht, U., Abelian Groups with Semi-Simple Artinian Quasi-Endomorphism Rings, Rocky Mountain Journal of Mathematics, 24(1994), 853-866.
Arnold, D.M., Lady, L., Endomorphism rings and direct sums of torsion-free Abelian groups, Trans. Amer. Math. Soc., 211(1975), 225-237.
Arnold, D.M., and Murley, C.E., Abelian groups A, such that Hom(A;-) preserves direct sums of copies of A, Pac. J. Math., 56(1975), 7-20.
Arnold, D. M., Finite Rank Torsion Free Abelian Groups and Rings, Lecture Notes in Mathematics, Vol. 931, Springer-Verlag Berlin-Heidelberg-New York, 1982.
Chatters, A.W., Hajarnavis, C.R., Rings with Chain Conditions, Pitman Advanced Publishing 44, Boston, London, Melbourne, 1980.
Eklof, P.C., Mekler, A.H., Almost free Modules, Vol. 46, North Holland Mathematical Library, 1990.
Eklof, P.C, Mekler, A.H., Shelah, S., Uniformization and the diversity of Whitehead groups, Israel J. Math., 80(1992), 301-321.
Fuchs, L., Infinite Abelian Groups, vol. 1 and 2, Academic Press, New York and London, 1970/73.
Gobel, R., Trlifaj, J., Approximations and Endomorphism Algebras of Modules, vol. I and II, Expositions in Mathematics 41, De Gruyter, 2012.
Jans, J., Rings and Homology, Holt, Rinehart, and Winston, 1963.
Stenstrom, B., Rings of Quotients, Lecture Notes in Math. 217, Springer Verlag, Berlin, Heidelberg, New York, 1975.
Ulmer, F., A flatness criterion in Grothendieck categories, Inv. Math., 19(1973), 331-336.
Warfield, R.B., Jr., Homomorphisms and duality for torsion-free groups, Math. Z., 107(1968), 189-200.
Zemlicka, J., When products of self-small modules are self-small, Comm. Alg., 36(2008), no. 7, 2570-2576.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2015 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
