A general version of standard basis and its application to T-ideals. (Q2386463)

The paper under review discusses a general notion of the concept of a standard basis, with attention to the case of T-ideals in the free associative algebra. This leads to a stronger version of the famous Specht Problem whether in characteristic 0, every T-ideal is finitely based. Recall that this problem was solved in the affirmative by \textit{A. R. Kemer} [Ideals of identities of associative algebras (1991; Zbl 0732.16001)]. Furthermore, the author shows that the product of \(m\) commutators (in characteristic 0) is strongly Spechtian, that is, every T-ideal containing it, has a finite standard basis. A general open problem is stated: Does every T-ideal in characteristic 0 possess a finite standard basis?