Browsing by Author "Madran, Ugur"

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Citation - WoS: 3
Citation - Scopus: 3
On Generalized Invariants of Cyclic Groups
(Elsevier Science Bv, 2015) Erkuş, DENİZ ERDEMİRCİ; Madran, Ugur
In this paper, we extend the definition of generalized invariants for any finite group. Further, we describe the structure of generalized invariants of a cyclic group for lower dimensional indecomposable representations in the modular case, where the characteristic of the ground field divides the group order. Finally, an analog of a conjecture about Hilbert ideals associated with invariant rings has been proven for the case of generalized invariants. (C) 2014 Elsevier B.V. All rights reserved.
On Generators of the Hilbert Ideal for Cyclic Groups in Modular Invariant Theory
(Academic Press Inc Elsevier Science, 2015) Erkuş, DENİZ ERDEMİRCİ; Madran, Ugur
Let G be a cyclic group of order p(2) and V be a faithful indecomposable representation of G over a field F of characteristic p. We show that the Hilbert ideal of the invariant ring is generated by polynomials of degree at most |G| whenever dim V <= 4p or dim V >= p(2) - 2p, proving a conjecture of Derksen and Kemper in this particular case. (C) 2014 Elsevier Inc. All rights reserved.
Citation - WoS: 1
Citation - Scopus: 1
The Structure of Modular Generalized Invariants
(Elsevier Science Bv, 2016) Erkuş, DENİZ ERDEMİRCİ; Madran, Ugur
Let G be a finite group with a faithful representation V over a field F of odd characteristic p, where the order of G is divisible by p. In this article, it is proved that the generalized invariant module of G coincides with the (polynomial) invariant ring of the representation under a necessary and sufficient group theoretical condition. Moreover, the structure of the generalized invariant module for any finite group is determined, providing a tool for computing this module. (C) 2016 Elsevier B.V. All rights reserved.