Varijeteti grupoida

Abstract

Ova teza se bavi ¤-kvazilinearnim varijetetima grupoida. Pokazano je da postoji ta·cno dvadeset osam idempotentnih ¤-kvazilinearnih varijeteta grupoida, od kojih dvadeset ·sest varijeteta imaju kona·cnu bazu i te baze su i navedene, dok preostala dva varijeteta imaju inherentno beskona·cnu bazu. U tezi je opisano ured enje svih idempotentnih ¤-kvazilinearnih varijeteta grupoida i nalazimo male grupoide koji generi·su svaki od navedenih varijeteta. Na kraju je pokazano da postoji kontinum mnogo ¤-kvazilinearnih variejeteta grupoida.

The topic of this thesis are ¤-quasilinear varieties of groupoids. We show that there exist exactly twenty-eight idempotent ¤-quasilinear varieties of groupoids, twenty-six of which are ¯nitely based (and we explicitly give ¯nite bases for each of them), while two are inherently non¯nitely based. We describe the ordering of these twenty-eight idempotent ¤-quasilinear varieties of groupoids and ¯nd small generating algebras for each of them. In the end we show that there exist continuum many ¤-quasilinear varieties of groupoids, not all of which are even locally ¯nite.