Abstract
Since the end of sixties and up to date a number of examples of algebraic objects without the finite basis property have been constructed (for groups, Lie algebras and certain other rings close to associative). On the other hand for associative rings and several other class of rings a number of positive results were obtained. For finite rings this is the theorem of Lvov and Kruse [1, 2], for algebras over a field of characteristic 0 this is Kemer’s Theorem (see [3]), for T-spaces over fields of characteristic 0 this is author’s result (see [4]).
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