Keywords and phrases: torsion free module, integral domain, separable module, quasi-isomorphism, torsion free abelian group.
Received: July 27, 2022; Revised: October 14, 2022; Accepted: October 18, 2022; Published: November 2, 2022
How to cite this article: E. F. Cornelius, Jr., 1-separable torsion free modules over integral domains, JP Journal of Algebra, Number Theory and Applications 59 (2022), 1-16. http://dx.doi.org/10.17654/0972555522035
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] R. Baer, Abelian groups without elements of finite order, Duke Math. J. 3 (1937), 68-122. [2] R. A. Beaumont and R. S. Pierce, Torsion free groups of rank two, Mem. Amer. Math. Soc. 38 (1961), 41 pp. [3] E. F. Cornelius, Jr., A sufficient condition for separability, J. Algebra 67(2) (1980), 476-478. https://www.sciencedirect.com/science/article/pii/0021869380901714. [4] E. F. Cornelius, Jr., Characterization of a class of torsion free groups in terms of endomorphisms, Pacific J. Math. 79(2) (1978), 341-355. Submission date corrected to February 5, 1974, Pacific J. Math. 85(2) (1979), 501. [5] E. F. Cornelius, Jr., A generalization of separable groups, Pacific J. Math. 39(3) (1970), 603-613. [6] László Fuchs, Abelian Groups, Springer, Switzerland, 2015. [7] László Fuchs and Jorge E. Macías-Díaz, On completely decomposable and separable modules over Prüfer domains, J. Comm. Alg. 2(2) (2010), 159-176. [8] L. Fuchs and G. Viljoen, A generalization of separable torsion-free abelian groups, Rend. Sem. Mat. Univ. Padova 73 (1985), 15-21. [9] Rüdiger Göbel, László Fuchs - a personal evaluation of his contributions to mathematics, Period. Math. Hungar. 32(1-2) (1996), 13-29. [10] G. Kolettis, Jr., Homogeneously decomposable modules, Studies on Abelian Groups, Springer-Verlag, 1968, pp. 223-238. [11] E. Lee Lady, Finite Rank Torsion Free Modules over Dedekind Domains, University of Hawaii, 1998. http://www.math.hawaii.edu/~lee/book/. [12] C. Metelli, On type-related properties of torsionfree abelian groups, Abelian Group Theory, R. Göbel, L. Lady and A. Mader, eds., Lecture Notes in Mathematics, Springer-Verlag, Vol. 1006, 1983, pp. 253-267. [13] Bruce Olberding, Prüfer domains and pure submodules of direct sums of ideals, Mathematika 46 (1999), 425-432. [14] Bruce Olberding, Characterizations and constructions of h-local domains, Contributions to Module Theory, Walter de Gruyter, 2007, pp. 1-21. [15] K. M. Rangaswamy, On C-separable Abelian groups, Comm. Algebra 13(6) (1985), 1219-1227. [16] J. D. Reid and W. J. Wickless, Ross Allen Beaumont (in Memoriam), Abelian Groups and Modules, Paul C. Eklof and Rüdiger Göbel, eds., International Conference in Dublin, August 10-14, 1998, Birkhauser Boston, 1999.
|