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Öğe Grobner-Shirshov Bases of the Generalized Bruck-Reilly *-Extension(WORLD SCIENTIFIC PUBL CO PTE LTD, 2012) Kocapınar, Canan; Karpuz, Eylem Güzel; Ateş, Fırat; Çevik, A. SinanIn this paper we first define a presentation for the generalized Bruck-Reilly *-extension of a monoid and then we work on its Grobner-Shirshov bases.Öğe A new example of strongly pi inverse monoids(2011) Karpuz, Eylem Güzel; Çevik, Ahmet SinanIn [1], Ate¸s defined the semidirect product version of the Schützenberger product for any two monoids, and examined its regularity. Since this is a new product and there are so many algebraic properties that need to be checked for it, in this paper we determine necessary and sufficient conditions for this new version to be strongly pi-inverse, and then give some results.Öğe On the Efficiency of Semi-Direct Products of Finite Cyclic Monoids by One-Relator Monoids(Amer Inst Physics, 2010) Ateş, Fırat; Karpuz, Eylem Güzel; Güngör, A. Dilek; Çevik, A. Sinan; Cangül, İsmail NaciIn this paper we give necessary and sufficient conditions for the efficiency of a standard presentation for the semi-direct product of finite cyclic monoids by one-relator monoids.Öğe On the Norms of Toeplitz and Hankel Matrices With Pell Numbers(Amer Inst Physics, 2010) Karpuz, Eylem Güzel; Ateş, Fırat; Güngör, A. Dilek; Cangül, İsmail Naci; Çevik, A. SinanLet us define A = [a(ij)](i,j=0)(n-1) and B = [b(ij)](i,j=0)(n-1) as n x n Toeplitz and Hankel matrices, respectively, such that a(ij) = Pi-j and b(ij) = Pi+j, where P denotes the Pell number. We present upper and lower bounds for the spectral norms of these matrices.Öğe On the Solvability of Word Problem by Adian Graphs(2012) Karpuz, Eylem Güzel; Çevik, Sinan AhmetThe purpose of this paper is to determine some forms of the relations in a finite semigroup presentation with zero deficiency which have solvable word problem via Adian graphs.Öğe A presentation and some finiteness conditions for a new version of the schützenberger product of monoids(2016) Karpuz, Eylem Güzel; Ateş, Fırat; Çevik, Ahmet Sinan; Cangül, İsmail NaciIn this paper we first define a new version of the Sch¨utzenberger product for any two monoids A and B , and then, by defining a generating and relator set, we present some finite and infinite consequences of the main result. In the final part of this paper, we give necessary and sufficient conditions for this new version to be periodic and locally finite.Öğe Rewriting as a Special Case of Noncommutative Gröbner Bases Theory for the Affine Weyl Group An(Birkhauser Boston, 2010) Çevik, Ahmet Sinan; Özel, Cenap; Karpuz, Eylem GüzelThe aim of this work is to find Grobner-Shirshov bases of the affine Weyl group of type (A(n)) over tilde (n >= 2) from the point of complete rewriting systems.