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We show that if $k$ is a countable field, then there exists a finitely generated, infinite-dimensional, primitive algebraic $k$-algebra $A$ whose Gelfand-Kirillov dimension is at most six. In addition to this we construct a two-generated primitive algebraic $k$-algebra. We also pose many open problems.
|Title of host publication||New Trends in Noncommutative Algebra|
|Subtitle of host publication||A Conference in Honor of Ken Goodearl’s 65th Birthday|
|Editors||P Ara, K. A. Brown, T. H. Lenagan, E. S. Letzter, J. T. Stafford, J. J. Zhang|
|Publisher||American Mathematical Society|
|Number of pages||12|
|Publication status||Published - 2012|
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- 1 Finished
Nil algebras, algebraic algebras and algebras with finite Gelfand-Kirillov dimension
1/08/06 → 31/07/11