The representation type of tensor product algebras of finite-dimensional algebras is considered. The characterization of algebras A, B such that A⊗B is of tame representation type is given in terms of the Gabriel quivers of the algebras A, B. Introduction. In this paper by an algebra we mean a finite-dimensional algebra over a fixed algebraically closed field K. All algebras are assumed to be b...

One of the major open problems in automata and logic is the following: is there an algorithm which inputs a regular tree language and decides if the language can be defined in first-order logic? The goal of this paper is to present this problem and similar ones using the language of universal algebra, highlighting potential connections to the structural theory of finite algebras, including Tame...

This paper surveys results concerning the quantization approach to Jacobian Conjecture and related topics on noncommutative algebras. We start with a brief review of its motivations. The first section deals approximation by tame automorphisms Belov–Kontsevich Conjecture. second provides proof Bergman’s centralizer theorem which has not been revisited for almost 50 years formulates several probl...

In this paper, we study the maximal length of green sequences for quivers type \(\widetilde{{\mathbf {D}}}\) and {E}}}\) by using theory tilting mutation. We show that does not depend on choice orientation determine it explicitly. Moreover, give a program which counts all given Dynkin/extended Dynkin quiver.