4 citations · 11 across the 10 of their papers we have counts for
15 papers
On the Nowicki Conjecture for the free Lie algebra of rank 2
Lucio Centrone, Sehmus Findik, Manuela da Silva Souza
Let K[X_n]=K[x_1,\ldots,x_n] be the polynomial algebra in n variables over a field K of characteristic zero. A locally nilpotent linear derivation δof K[X_n] is called Weitzenböck…
Generalizations of almost prime and right -prime ideals in noncommutative rings
Alaa Abouhalaka, Sehmus Findik, Nico Groenewald
Let be a noncommutative ring, and let be an -system of . In this paper, we give more results on the concept of almost prime (right) ideals, that were introduced by th…
Almost prime ideals in noncommutative rings
Alaa Abouhalaka, Sehmus Findik
A proper ideal of a commutative ring with identity is an almost prime ideal if implies or . In this paper we define almost prime ide…
On Nowicki's conjecture: a survey and a new result
Lucio Centrone, Andre Dushimirimana, Sehmus Findik
The goal of the paper is twofold: it aims to give an extensive set of tools and bibliography towards Nowicki's conjecture both in an associative setting; it establishes a new resul…
Symmetric polynomials in the variety generated by Grassmann algebras
Nazan Akdogan, Sehmus Findik
Let denote the variety generated by infinite dimensional Grassmann algebras; i.e., the collection of all unitary associative algebras satisfying the identity $[[z_1,z…
Symmetric polynomials in Leibniz algebras and their inner automorphisms
Sehmus Findik, Zeynep Ozkurt
Let be the free metabelian Leibniz algebra generated by the set over a field of characteristic zero. This is the free algebra of rank in the…
Inner automorphisms of Lie algebras of symmetric polynomials
Sehmus Findik, Nazar Sahin Oguslu
Let be the free Lie algebra, be the free metabelian Lie algebra, and be the free metabelian nilpotent of class Lie algebra of rank generated by $x…
Symmetric polynomials in the free metabelian Lie algebras
Vesselin Drensky, Sehmus Findik, Nazar Sahin Oguslu
Let be the commutative polynomial algebra in the variables over a field of characteristic zero. A theorem from undergraduate course of algebra…
The Nowicki Conjecture for relatively free algebras
Lucio Centrone, Sehmus Findik
A linear locally nilpotent derivation of the polynomial algebra in variables over a field of characteristic 0 is called a Weitzenböck derivation. It is well known…
Classical invariant theory for free metabelian Lie algebras
Vesselin Drensky, Sehmus Findik
Let be a vector space with basis over a field of characteristic 0. One of the main topics of classical invariant theory is the study of the alge…
Weitzenboeck derivations of free metabelian associative algebras
Rumen Dangovski, Vesselin Drensky, Sehmus Findik
By the classical theorem of Weitzenboeck the algebra of constants (i.e., the kernel) of a nonzero locally nilpotent linear derivation of the polynomial algebra K[X] in d variables…
Weitzenboeck derivations of free metabelian Lie algebras
Rumen Dangovski, Vesselin Drensky, Sehmus Findik
A nonzero locally nilpotent linear derivation of the polynomial algebra K[X] in d variables over a field K of characteristic 0 is called a Weitzenboeck derivation. The classical th…
Inner Automorphisms of Lie Algebras Related with Generic 2 x 2 Matrices
Vesselin Drensky, Sehmus Findik
Let F_m=F_m(var(sl(2,K))) be the relatively free algebra of rank m in the variety of Lie algebras generated by the algebra sl(2,K) over a field K of characteristic 0. Translating a…
Normal and normally outer automorphisms of free metabelian nilpotent Lie algebras
Sehmus Findik
Let L be the free m-generated metabelian nilpotent of class c Lie algebra over a field of characteristic 0. An automorphism f of L is called normal if f(I)=I for every ideal I of t…
Inner and Outer Automorphisms of Free Metabelian Nilpotent Lie algebras
Vesselin Drensky, Sehmus Findik
We describe the groups of inner and outer automorphisms of the free metabelian nilpotent Lie algebra of finite rank over a field of characteristic 0. To obtain this result we first…