Department of Mathematics
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On m-th roots of nilpotent matrices
Öztürk, Semra (2021-11-01)
A new necessary and sufficient condition for the existence of an m-th root of a nilpotent matrix in terms of the multiplicities of Jordan blocks is obtained and expressed as a system of linear equations with nonnegative in...
Öztürk, Semra (2018-01-01)
Let A and B be matrices which are polynomials in r pairwise commuting nilpotent matrices over a field. We give a sufficient condition for the null space of A(i) to equal that of B-i for all i, in particular, for A and B to...
Restricted Modules and Conjectures on Modules of Constant Jordan Type
Öztürk, Semra (Springer, 2014-01-01)
We introduce the class of restricted k[A]-modules and p t-Jordan types for a finite abelian p-group A of exponent at least p t and a field k of characteristic p. For these modules, we generalize several theorems by Benson,...
Öztürk, Semra (2011-01-01)
We study finitely generated modules over k[G] for a finite abelian p-group G, char (k) = p, through restrictions to certain subalgebras of k[G]. We define p-power points, shifted cyclic p-power order subgroups of k[G], and...
Jordan type of a k[C(p)xC(p)]-module
Öztürk, Semra (2011-01-01)
Let E be the elementary abelian group C(p)xC(p), k a field of characteristic p, M a finite dimensional module over the group algebra k[E] and J the Jacobson radical J of k[E]. We prove that the decomposition of M when cons...
Commuting Nilpotent Operators and Maximal Rank
Öztürk, Semra (Springer Science and Business Media LLC, 2010-01-01)
Let X, (X) over tilde be commuting nilpotent matrices over k with nilpotency p(t), where k is an algebraically closed field of positive characteristic p. We show that if X - (X) over tilde is a certain linear combination o...
Structure and Detection Theorems for k[C2xC4]-modules
Öztürk, Semra (European Mathematical Society Publishing House, 2010-01-01)
Controlled assemble and microfabrication of zeolite particles on SiO2 substrates for potential biosensor applications
Öztürk, Semra; Turan, Raşit; Akata Kurç, Burcu (2008-12-04)
Zeolite nanoparticles were organized into functional entities on SiO2 substrates and microfabrication technique was tested to form patterns of zeolite nanoparticles on SiO2 using the electron beam lithography (EBL). The ef...
Betti numbers of fixed point sets and multiplicities of indecomposable summands
Öztürk, Semra (Cambridge University Press (CUP), 2003-04-01)
Let G be a finite group of even order, k be a field of characteristic 2, and M be a finitely generated kG-module. If M is realized by a compact G-Moore space X, then the Betti numbers of the fixed point set X-Cn and the mu...
A note on a theorem of Dwyer and Wilkerson
Öztürk, Semra (Springer Science and Business Media LLC, 2001-01-03)
We prove a version of Theorem 2.3 in [1] for the non-elementary abelian group Z(2) x Z(2n), n greater than or equal to 2. Roughly, we describe the equivariant cohomology of (union of) fixed point sets as the unstable part ...
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