We establish when the partial orders and coincide for all modules of the same dimension from the additive category of a generalized standard almost cyclic coherent component of the Auslander-Reiten quiver of a finite-dimensional algebra.
We develop a new combinatorial method to deal with a degree estimate for subalgebras generated by two elements in different environments. We obtain a lower bound for the degree of the elements in two-generated subalgebras of a free associative algebra over a field of zero characteristic. We also reproduce a somewhat refined degree estimate of Shestakov and Umirbaev for the polynomial algebra, which plays an essential role in the recent celebrated solution of the Nagata conjecture and the strong...
The goal of this paper is to provide some basic structure information on derivations in finite semirings.
We discuss range inclusion results for derivations on noncommutative Banach algebras from the point of view of ring theory.
Let be a prime ring, a nonzero ideal of , a derivation of and fixed positive integers. (i) If for all , then is commutative. (ii) If and for all , then is commutative. Moreover, we also examine the case when is a semiprime ring.
Let be a prime ring of char with a nonzero derivation and let be its noncentral Lie ideal. If for some fixed integers , for all , then satisfies , the standard identity in four variables.
Comparing the bounded derived categories of an algebra and of the endomorphism algebra of a given support -tilting module, we find a relation between the derived dimensions of an algebra and of the endomorphism algebra of a given -tilting module.