ИСТИНА

The general Specht problem says "does a given set of identities of associative algebras stabilize? i.e., does any set of identities can be deduced from a finite subset? Specht kept in mind the case of the field of characteristic zero, and this problem was solved by A.R. Kemer in an affirmative way. In positive characteristics for the case of finite number of variables A. Belov Rowen Vishnu gave an affirmative answer andin general counterexamples were constructed. The general Specht problem is one of the central problems in polynomial identity theory. Its solution gave a technique related with some point of view on noncommutative algebraic geometry and representation theory to solve some other open questions, including new insights in representation theory (how semisimple components interact with each other via radical). The counterexamples in positive characteristics and Kemers proof of finite basis property in characteristic zero connected with some deep properties of Grassman algebra and, by the way, give us a chance to build a supertheory in characteristic 2.