Let A be a finite dimensional hereditary algebra over an algebraically closed field k, A(m) be the m-replicated algebra of A and Cm(A) be the m-cluster category of A. We investigate properties of complements to a faithful almost complete tilting A(m)-module and prove that the m-cluster mutation in Cm(A) can be realized in mod A (m), which generalizes corresponding results on duplicated algebras...

To every Poisson algebraic variety X over an algebraically closed field of characteristic zero, we canonically attach a right D-module M(X) on X . If X is affine, solutions of M(X) in the space of algebraic distributions on X are Poisson traces on X , i.e., distributions invariant under Hamiltonian flows. When X has finitely many symplectic leaves, we prove that M(X) is holonomic. Thus, when X ...

It is proved that if A is aregular uniform algebra on a compact Hausdorff space X in which every closed ideal is an M-ideal, then A = C(X).

We generalize the universal power series of Seleznev to several variables and we allow coefficients depend on parameters. Then, approximable functions may same The approximation holds products $$K = \displaystyle \prod \nolimits _{i 1}^d K_i$$ , where $$K_i \subseteq \mathbb {C}$$ are compact sets $$\mathbb {C} {\setminus } connected, $$i 1, \ldots d$$ $$0 \notin K$$ . On such K partial sums ap...