L�PLIKE ARITMEETILISTE ALGEBRATE KATEGOORSEST EKVIVALENTSIST/ ON CATEGORICAL EQUIVALENCE OF FINITE ARITHMETICAL ALGEBRAS
Ettekannete seerias kavatsetakse anda selliste l�plike algebrate kirjeldus kategoorse ekvivalentsi t�psuseni, mis 1) ei oma p�risalamalgebraid, 2) ei oma erinevaid isomorfseid faktoralgebraid ja 3) tekitavad aritmeetilise muutkonna. Avaettekandes tutvustatakse k�igepealt kategoorse ekvivalentsi m�istet ja tema kohta k�ivaid �ldisi tulemusi ning ka C. Bergmani tulemust, mis k�sitleb enamustermiga algebraid. Seej�rel vaadeldakse �lalmainitud erijuhule ja n�idatakse, et need algebrad on kategoorselt ekvivalentsed parajasti siis, kui nende nn r�hmskeemid on isomorfsed.
In the series of talks we try to give a characterization up to equivalence of finite algebras which 1) do not have proper subalgebras, 2) do not have different isomorphic quotient algebras, and 3) generate an arithmetical variety. In the first talk, the notion of categorical equivalence is presented together with general results about it, including C. Bergman's result, which concerns algebras having majority term. After that we consider abovementioned special cases and show that these algebras are categorically equivalent if and only if their so called group schemes are isomorphic.