scholarly journals The torsion‐free part of the Ziegler spectrum of orders over Dedekind domains

2020 ◽  
Vol 66 (1) ◽  
pp. 20-36
Author(s):  
Lorna Gregory ◽  
Sonia L'Innocente ◽  
Carlo Toffalori
Keyword(s):  
Free Part ◽  
Dedekind Domains ◽  
Ziegler Spectrum ◽  
Torsion Free

scholarly journals The torsion-free part of the Ziegler spectrum of the Klein four group

2011 ◽  
Vol 215 (8) ◽  
pp. 1791-1804 ◽  
Author(s):  
Gena Puninski ◽  
Carlo Toffalori
Keyword(s):  
Free Part ◽  
Ziegler Spectrum ◽  
Torsion Free

Arithmetic modules over generalized Dedekind domains

2020 ◽  
pp. 2250045
Author(s):  
Indah Emilia Wijayanti ◽  
Hidetoshi Marubayashi ◽  
Iwan Ernanto ◽  
Sutopo
Keyword(s):  
Free Module ◽  
Dedekind Domain ◽  
Finitely Generated ◽  
Multiplication Module ◽  
Dedekind Domains ◽  
Torsion Free Module ◽  
Polynomial Module ◽  
Torsion Free

Let [Formula: see text] be a finitely generated torsion-free module over a generalized Dedekind domain [Formula: see text]. It is shown that if [Formula: see text] is a projective [Formula: see text]-module, then it is a generalized Dedekind module and [Formula: see text]-multiplication module. In case [Formula: see text] is Noetherian it is shown that [Formula: see text] is either a generalized Dedekind module or a Krull module. Furthermore, the polynomial module [Formula: see text] is a generalized Dedekind [Formula: see text]-module (a Krull [Formula: see text]-module) if [Formula: see text] is a generalized Dedekind module (a Krull module), respectively.

scholarly journals The group of endotrivial modules for the symmetric and alternating groups

2010 ◽  
Vol 53 (1) ◽  
pp. 83-95 ◽  
Author(s):  
Jon F. Carlson ◽  
David J. Hemmer ◽  
Nadia Mazza
Keyword(s):  
Modular Group ◽  
Symmetric Groups ◽  
Group Algebras ◽  
Torsion Subgroup ◽  
Alternating Groups ◽  
Free Part ◽  
Rank 2 ◽  
Torsion Free

AbstractWe complete a classification of the groups of endotrivial modules for the modular group algebras of symmetric groups and alternating groups. We show that, for n ≥ p2, the torsion subgroup of the group of endotrivial modules for the symmetric groups is generated by the sign representation. The torsion subgroup is trivial for the alternating groups. The torsion-free part of the group is free abelian of rank 1 if n ≥ p2 + p and has rank 2 if p2 ≤ n < p2 + p. This completes the work begun earlier by Carlson, Mazza and Nakano.

Semi-irreducible Zariski spaces of modules

2014 ◽  
Vol 13 (08) ◽  
pp. 1450054
Author(s):  
A. Nikseresht ◽  
A. Azizi
Keyword(s):  
Dedekind Domain ◽  
Finitely Generated ◽  
Dedekind Domains ◽  
The Family ◽  
Finitely Generated Modules ◽  
Torsion Free

In this paper, we state conditions under which, the family of semi-irreducible submodules of a module determine a Zariski space of that module and study the properties of this space. Also we characterize semi-irreducible submodules of finitely generated modules over Dedekind domains. Moreover, assuming that M and M′ are finitely generated modules over a Dedekind domain having isomorphic semi-irreducible Zariski spaces, we find some common properties of M and M′. In particular, we show that in this case the torsion-free components of M and M′ have the same rank and the torsion submodules of [Formula: see text] and [Formula: see text] are isomorphic, where N and N′ are the intersection of all semi-irreducible submodules of M and M′, respectively.

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