Some Decidability Results for ℤ[G]‐Modules when G is Cyclic of Squarefree Order

Mathematical Logic Quarterly 42 (1):433-445 (1996)
  Copy   BIBTEX

Abstract

We extend the analysis of the decision problem for modules over a group ring ℤ[G] to the case when G is a cyclic group of squarefree order. We show that separated ℤ[G]-modules have a decidable theory, and we discuss the model theoretic role of these modules within the class of all ℤ[G]-modules. The paper includes a short analysis of the decision problem for the theories of modules over ℤ[ζm], where m is a positive integer and ζm is a primitive mth root of 1

Categories

Keywords

Reprint years

DOI

10.1002/malq.19960420135

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,219

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

Decidability for ℤ[G]‐Modules when G is Cyclic of Prime Order.Carlo Toffalori - 1996 - Mathematical Logic Quarterly 42 (1):369-378.
Comparing First Order Theories of Modules over Group Rings II: Decidability: Decidability.Carlo Toffalori & S. Cittadini - 2002 - Mathematical Logic Quarterly 48 (4):483-498.
Comparing First Order Theories of Modules over Group Rings.Saverio Cittadini & Carlo Toffalori - 2002 - Mathematical Logic Quarterly 48 (1):147-156.
The model completion of the theory of modules over finitely generated commutative algebras.Moshe Kamensky - 2009 - Journal of Symbolic Logic 74 (3):734-750.
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.
Decidability for ℤ2G‐lattices when G Extends the Noncyclic Group of Order 4.Annalisa Marcja & Carlo Toffalori - 2002 - Mathematical Logic Quarterly 48 (2):203-212.
Deissler Rank Complexity of Powers of Indecomposable Injective Modules.R. Chartrand & T. Kucera - 1994 - Notre Dame Journal of Formal Logic 35 (3):398-402.
The decision problem for {vec Z}C(p^3)-lattices with p prime.Carlo Toffalori - 1998 - Archive for Mathematical Logic 37 (2):127-142.
The theory of {vec Z}C(2)^2-lattices is decidable.Stefano Baratella & Carlo Toffalori - 1998 - Archive for Mathematical Logic 37 (2):91-104.
ℵ0-categorical modules.Walter Baur - 1975 - Journal of Symbolic Logic 40 (2):213 - 220.
Pure-injectivity and model theory for G-sets.Ravi Rajani & Mike Prest - 2009 - Journal of Symbolic Logic 74 (2):474-488.
Vaught's conjecture for modules over a serial ring.Vera Puninskaya - 2000 - Journal of Symbolic Logic 65 (1):155-163.
Equivalence elementaire et decidabilite pour Des structures du type groupe agissant sur un groupe abelien.Patrick Simonetta - 1998 - Journal of Symbolic Logic 63 (4):1255-1285.
Motives for perfect PAC fields with pro-cyclic Galois group.Immanuel Halupczok - 2008 - Journal of Symbolic Logic 73 (3):1036-1050.
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.

Analytics

Added to PP
2013-12-01

Downloads
5 (#1,469,565)

6 months
1 (#1,459,555)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

An undecidability theorem for lattices over group rings.Carlo Toffalori - 1997 - Annals of Pure and Applied Logic 88 (2-3):241-262.

Add more citations

References found in this work

Model Theory and Modules.Mike Prest - 1989 - Journal of Symbolic Logic 54 (3):1115-1118.

Add more references