Abakarov, A. Sh.; Yakovlev, A. V. Identities of a triangular extension. (Russian) Zbl 0536.16022 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 132, 5-11 (1983). Let F be a field, let A and B be associative F-algebras with unit, let T(A) and T(B) be the T-ideals of identities of A and B in the free algebra \(F[x_ 1,...,x_ n]\) and let M be an (A,B)-bimodule. The algebra \(\begin{pmatrix} A & M \\ 0 & B \end{pmatrix}\) of triangular matrices \(\begin{pmatrix} \alpha & \mu \\ 0 & \beta \end{pmatrix}\), \(\alpha\in A\), \(\mu\in M\), \(\beta\in B\), is considered. Based on the methods of homological algebra and on the representation theory of algebras, the authors seek for conditions, under which the relation \(T\left(\begin{pmatrix} A & M \\ 0 & B \end{pmatrix}\right)=T(A)\cdot T(B)\) holds. In particular, they prove that this relation is true for all algebras A and B and for an (A,B)-bimodule M, which generates the category of (A,B)-bimodules. Reviewer: U.Kaljulaid Cited in 1 Review MSC: 16Rxx Rings with polynomial identity 16Exx Homological methods in associative algebras 16S50 Endomorphism rings; matrix rings Keywords:T-ideals of identities; triangular matrices × Cite Format Result Cite Review PDF Full Text: EuDML