Finitely presented quadratic algebras of intermediate growth

In this article, we give two examples of finitely presented quadratic algebras (algebras presented by quadratic relations) of intermediate growth.
Algebra and Discrete Mathematics


Kummer extensions of function fields with many rational places
Gülmez Temur, Burcu; Özbudak, Ferruh; Department of Mathematics (2005)
In this thesis, we give two simple and effective methods for constructing Kummer extensions of algebraic function fields over finite fields with many rational places. Some explicit examples are obtained after a practical search. We also study fibre products of Kummer extensions over a finite field and determine the exact number of rational places. We obtain explicit examples with many rational places by a practical search. We have a record (i.e the lower bound is improved) and a new entry for the table of v...
On maximal curves and linearized permutation polynomials over finite fields
Özbudak, Ferruh (Elsevier BV, 2001-08-08)
The purpose of this paper is to construct maximal curves over large finite fields using linearized permutation polynomials. We also study linearized permutation polynomials under finite field extensions.
Characterisation and enumeration of a class of semi bent quadratic Boolean functions
KOÇAK, Neşe; Koçak, Onur Ozan; Özbudak, Ferruh; SAYGI, ZÜLFÜKAR (2015-01-01)
In this paper, we consider semi-bentness of quadratic Boolean functions defined for even n and give the characterisation of these functions. Up to our knowledge, semi-bentness of this class has not been investigated before and we proved that semi-bent functions of this form exist only for 6|n. Furthermore, we present a method for enumeration of semi-bent and bent functions in certain classes. Using this method we find the exact number of semi-bent functions of this form. Moreover, we complete some previous ...
Regularities in noncommutative Banach algebras
Dosiev, Anar (Springer Science and Business Media LLC, 2008-07-01)
In this paper we introduce regularities and subspectra in a unital noncommutative Banach algebra and prove that there is a correspondence between them similar to the commutative case. This correspondence involves a radical on a class of Banach algebras equipped with a subspectrum. Taylor and Slodkowski spectra for noncommutative tuples of bounded linear operators are the main examples of subspectra in the noncommutative case.
On algebraic K-theory of real algebraic varieties with circle action
Ozan, Yıldıray (Elsevier BV, 2002-05-24)
Assume that X is a compact connected orientable nonsingular real algebraic variety with an algebraic free S-1-action so that the quotient Y=X/S-1 is also a real algebraic variety. If pi:X --> Y is the quotient map then the induced map between reduced algebraic K-groups, tensored with Q, pi* : (K) over bar (0)(R(Y, C)) circle times Q --> (K) over bar (0)(R(X, C)) circle times Q is onto, where R(X, C) = R(X) circle times C, R(X) denoting the ring of entire rational (regular) functions on the real algebraic va...
Citation Formats
D. Koçak Benli, “Finitely presented quadratic algebras of intermediate growth,” Algebra and Discrete Mathematics, pp. 69–88, 2015, Accessed: 00, 2021. [Online]. Available: