We state that all Rota-Baxter operators of nonzero weight on Grassmann algebra over a field characteristic zero are projections subalgebra along another one. show the one-to-one correspondence between solutions associative Yang-Baxter equation and matrix $M_n(F)$ (joint with P. Kolesnikov). prove unital (alternative, Jordan) algebraic nilpotent. For an $A$, we introduce its new invariant rb-ind...

We introduce the notion of locally finite decomposition rank, a structural property shared by many stably finite nuclear C∗-algebras. The concept is particularly relevant for Elliott’s program to classify nuclear C∗algebras by K-theory data. We study some of its properties and show that a simple unital C∗-algebra, which has locally finite decomposition rank, real rank zero and which absorbs the...