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Rings of invariants for modular representations of the Klein four group


Authors: Müfit Sezer and R. James Shank
Journal: Trans. Amer. Math. Soc. 368 (2016), 5655-5673
MSC (2010): Primary 13A50
DOI: https://doi.org/10.1090/tran/6516
Published electronically: December 3, 2015
MathSciNet review: 3458394
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Abstract: We study the rings of invariants for the indecomposable modular representations of the Klein four group. For each such representation we compute the Noether number and give minimal generating sets for the Hilbert ideal and the field of fractions. We observe that, with the exception of the regular representation, the Hilbert ideal for each of these representations is a complete intersection.


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Additional Information

Müfit Sezer
Affiliation: Department of Mathematics, Bilkent University, 06800 Ankara, Turkey
Email: sezer@fen.bilkent.edu.tr

R. James Shank
Affiliation: School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, CT2 7NF, United Kingdom
Email: R.J.Shank@kent.ac.uk

DOI: https://doi.org/10.1090/tran/6516
Received by editor(s): October 1, 2013
Received by editor(s) in revised form: July 16, 2014
Published electronically: December 3, 2015
Additional Notes: The first author was partially supported by a grant from TÜBITAK: 112T113
Article copyright: © Copyright 2015 American Mathematical Society