Access the full text.
Sign up today, get DeepDyve free for 14 days.
Françoise Point, M. Prest (1988)
Decidability for Theories of ModulesJournal of The London Mathematical Society-second Series
P. Hill, C. Megibben (1989)
Generalizations of the stacked bases theoremTransactions of the American Mathematical Society, 312
P. Schmitt (1982)
The Elementary Theory of Torsionfree Abelian Groups With a Predicate Specifying a SubgroupMath. Log. Q., 28
Jinzhong Xu (1996)
Flat covers of modules
I. Herzog (1993)
Elementary duality of modulesTransactions of the American Mathematical Society, 340
M. Ziegler (1984)
Model theory of modulesAnn. Pure Appl. Log., 26
W. Baur (1980)
On the elementary theory of quadruples of vector spacesAnnals of Mathematical Logic, 19
M. Prest (1987)
Model theory and representation type of algebrasStudies in logic and the foundations of mathematics, 124
L. Bican, R. Bashir, E. Enochs (2001)
All Modules Have Flat CoversBulletin of the London Mathematical Society, 33
G. Kozlov, A. Kokorin (1969)
Elementary theory of abelian groups without torsion, with a predicate selecting a subgroupAlgebra and Logic, 8
M. Prest (1988)
Model theory and modules
W. Baur (1976)
Undecidability of the theory of abelian groups with a subgroup, 55
E. Enochs (1963)
Torsion free covering modules, 14
The study of pairs of modules (over a Dedekind domain) arises from two different perspectives, as a starting step in the analysis of tuples of submodules of a given module, or also as a particular case in the analysis of Abelian structures made by two modules and a morphism between them. We discuss how these two perspectives converge to pairs of modules, and we follow the latter one to obtain an alternative approach to the classification of pairs of torsionfree objects. Then we restrict our attention to pairs of free modules. Our main results are that the theory of pairs of free Abelian groups is co-recursively enumerable, and that a few remarkable extensions of this theory are decidable.
Archive for Mathematical Logic – Springer Journals
Published: Sep 27, 2005
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.