Comparing First Order Theories of Modules over Group Rings

&
Mathematical Logic Quarterly 48 (1):147-156 (2002)
  Copy   BIBTEX

Abstract

We consider R-torsionfree modules over group rings RG, where R is a Dedekind domain and G is a finite group. In the first part of the paper [4] we compared the theory T of all R-torsionfree RG-modules and the theory T0 of RG-lattices , and we realized that they are almost always different. Now we compare their behaviour with respect to decidability, when RG-lattices are of finite, or wild representation type

Categories

Keywords

Reprint years

DOI

10.1002/1521-3870(200201)48:1

Other Versions

No versions found

Links

PhilArchive

    This entry is not archived by us. If you are the author and have permission from the publisher, we recommend that you archive it. Many publishers automatically grant permission to authors to archive pre-prints. By uploading a copy of your work, you will enable us to better index it, making it easier to find.

    Upload a copy of this work     Papers currently archived: 104,962

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Comparing First Order Theories of Modules over Group Rings II: Decidability.Saverio Cittadini & Carlo Toffalori - 2002 - Mathematical Logic Quarterly 48 (5):483-498.
The torsionfree part of the Ziegler spectrum of $RG$ when $R$ is a Dedekind domain and $G$ is a finite group.A. Marcja, M. Prest & C. Toffalori - 2002 - Journal of Symbolic Logic 67 (3):1126-1140.
The theory of {vec Z}C(2)^2-lattices is decidable.Stefano Baratella & Carlo Toffalori - 1998 - Archive for Mathematical Logic 37 (2):91-104.
Weakly minimal modules over integral group rings and over related classes of rings.Stefano Leonesi, Sonia L'Innocente & Carlo Toffalori - 2005 - Mathematical Logic Quarterly 51 (6):613-625.
Towards the decidability of the theory of modules over finite commutative rings.Gena Puninski & Carlo Toffalori - 2009 - Annals of Pure and Applied Logic 159 (1-2):49-70.
Decidability for ℤ2 G-lattices when G Extends the Noncyclic Group of Order 4.Annalisa Marcja & Carlo Toffalori - 2002 - Mathematical Logic Quarterly 48 (2):203-212.
Decidability for ℤ[G]‐Modules when G is Cyclic of Prime Order.Carlo Toffalori - 1996 - Mathematical Logic Quarterly 42 (1):369-378.
The torsion‐free part of the Ziegler spectrum of orders over Dedekind domains.Lorna Gregory, Sonia L'Innocente & Carlo Toffalori - 2020 - Mathematical Logic Quarterly 66 (1):20-36.

Analytics

Added to PP
2013-12-01

Downloads
27 (#912,623)

6 months
5 (#864,813)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

The decision problem for {vec Z}C(p^3)-lattices with p prime.Carlo Toffalori - 1998 - Archive for Mathematical Logic 37 (2):127-142.
An undecidability theorem for lattices over group rings.Carlo Toffalori - 1997 - Annals of Pure and Applied Logic 88 (2-3):241-262.

Add more references