LŐPLIKE ARITMEETILISTE ALGEBRATE KATEGOORSEST EKVIVALENTSIST/ ON CATEGORICAL EQUIVALENCE OF FINITE ARITHMETICAL ALGEBRAS

Ettekannete seerias kavatsetakse anda selliste lőplike algebrate kirjeldus kategoorse ekvivalentsi täpsuseni, mis 1) ei oma pärisalamalgebraid, 2) ei oma erinevaid isomorfseid faktoralgebraid ja 3) tekitavad aritmeetilise muutkonna. Avaettekandes tutvustatakse kőigepealt kategoorse ekvivalentsi mőistet ja tema kohta käivaid üldisi tulemusi ning ka C. Bergmani tulemust, mis käsitleb enamustermiga algebraid. Seejärel vaadeldakse ülalmainitud erijuhule ja näidatakse, et need algebrad on kategoorselt ekvivalentsed parajasti siis, kui nende nn rühmskeemid 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.