show/hide this revision's text 2 associative

As a warmup to this question you might want to think about the closure of semisimple associative algebras inside all finite dimensional asociative algebras of a given dimension. As a warmup to that question you might want to think about the commutative case. As a warmup to that question you might look at a beautiful paper by Bjorn Poonen (in particular, Section 6 and Remark 6.11).

show/hide this revision's text 1

As a warmup to this question you might want to think about the closure of semisimple algebras inside all finite dimensional algebras of a given dimension. As a warmup to that question you might want to think about the commutative case. As a warmup to that question you might look at a beautiful paper by Bjorn Poonen (in particular, Section 6 and Remark 6.11).