Schreier and Nielsen varieties
2006
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Advisor: Yrd. Doç. Dr. Ela Aydın
Abstract (EN)
ABSTRACTMSc THESISSCHREIER AND NIELSEN VARIETIESSaycan SOYERDEPARTMENT OF MATHEMATICSINSTITUTE OF NATURAL AND APPLIED SCIENCESUNIVERSITY OF ÇUKUROVASupervisor : Asist. Prof.Dr. Ela AYDINYears : 2006 , Pages : 36Jury : Prof.Dr. Naime EKİCİYrd.Doç.Dr. Ela AYDINYrd.Doç.Dr. Ersin KIRALA variety Ï of algebraic systems in which the subalgebras of free algebrasare again free is called a Schreier variety. If g1 ,..., g n generate a subalgebra G of thefree Ï - algebra F , then there is an effective procedure for obtaining a free set ofgenerators for G.It is proved that every finitely generated homogeneous subalgebras of free Ï -algebras are free Ï - algebras.Consequently it is obtained that every subalgebras offree Ï - algebras are again free. We?ve investigated that a variety of linear algebrasover an infinite field is a Schreier variety if and only if it is a Nielsen variety.Key Words : Schreier variety, Nielsen variety, free Lie algebras, homogeneoussubalgebras.II
Author
Saycan Soyer
How to Cite
Saycan Soyer (Master Thesis). Schreier and Nielsen varieties, 2006, Çukurova University.
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