The Free Product of Algebras with Standard Base for Ideals / Latyshev V.N. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2011. № 3. P. 19-23 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].
A wide class of associative algebras admitting standard bases of ideals was introduced in previous papers of the author. They are called algebras with strong filtration. This class includes all known examples of associative algebras whose ideals possess standard bases. It was proved by the author that the class of algebras with strong filtration is closed with respect to direct sums and tensorial products. It is shown in this paper that it is closed with respect to free products of algebras.
standard bases, algebras with strong filtration, free products of algebras.