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GK–DIMENSION OF ALGEBRAS WITH MANY GENERIC RELATIONS *
AGATA SMOKTUNOWICZ
Journal:

Glasgow Mathematical Journal / Volume 51 / Issue 2 / May 2009

Published online by Cambridge University Press:

01 May 2009, pp. 253-256

Print publication:

May 2009
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We prove some results on algebras, satisfying many generic relations. As an application we show that there are Golod–Shafarevich algebras which cannot be homomorphically mapped onto infinite dimensional algebras with finite Gelfand–Kirillov dimension. This answers a question of Zelmanov (Some open problems in the theory of infinite dimensional algebras, J. Korean Math. Soc. 44(5) 2007, 1185–1195).