ALMOST REGULAR AUSLANDER–REITEN COMPONENTS AND QUASITILTED ALGEBRAS

Almost Regular Auslander-reiten Components and Quasitilted Algebras

The problem of giving a general description of the shapes of AuslanderReiten components of an artin algebra has been settled for semiregular components (see [4, 9, 14]). Recently, S. Li has considered this problem for components in which every possible path from an injective module to a projective module is sectional. The result says that such a component is embeddable in some ZZ∆ with ∆ a quiv...

On Auslander–Reiten components for quasitilted algebras

An artin algebra A over a commutative artin ring R is called quasitilted if gl.dimA ≤ 2 and for each indecomposable finitely generated A-module M we have pdM ≤ 1 or idM ≤ 1. In [11] several characterizations of quasitilted algebras were proven. We investigate the structure and homological properties of connected components in the Auslander–Reiten quiver ΓA of a quasitilted algebra A. Let A be a...

Tilting Theory and Quasitilted Algebras

Regular, pseudo-regular, and almost regular matrices

We give lower bounds on the largest singular value of arbitrary matrices, some of which are asymptotically tight for almost all matrices. To study when these bounds are exact, we introduce several combinatorial concepts. In particular, we introduce regular, pseudo-regular, and almost regular matrices. Nonnegative, symmetric, almost regular matrices were studied earlier by Ho¤man, Wolfe, and Ho¤...

Almost n-Multiplicative Maps‎ between‎ ‎Frechet Algebras

For the Fr'{e}chet algebras $(A, (p_k))$ and $(B, (q_k))$ and $n in mathbb{N}$, $ngeq 2$, a linear map $T:A rightarrow B$ is called textit{almost $n$-multiplicative}, with respect to $(p_k)$ and $(q_k)$, if there exists $varepsilongeq 0$ such that$$q_k(Ta_1a_2cdots a_n-Ta_1Ta_2cdots Ta_n)leq varepsilon p_k(a_1) p_k(a_2)cdots p_k(a_n),$$for each $kin mathbb{N}$ and $a_1, a_2, ldots, a_nin A$. Th...