Standardly stratified lower triangular $\mathbb{K}$-algebras with enough idempotents

Abstract

In this paper we study the lower triangular matrix $\mathbb{K}$-algebra $\Lambda :=\left[\begin{array}{cc}T& 0\\ M& U\end{array}\right],$ where $U$ and $T$ are basic $\mathbb{K}$-algebras with enough idempotents and $M$ is an $U$-$T$-bimodule where $\mathbb{K}$ acts centrally. Moreover, we characterise in terms of $U,$ $T$ and $M$ when, on one hand, the lower triangular matrix $\mathbb{K}$-algebra $\Lambda$ is standardly stratified in the sense of the paper "A generalization theory of standardly stratified algebras I: Standardly stratified ringois"; and on another hand, when $\Lambda$ is locally bounded in the sense of the paper "Locally finite generated modules over rings with enough idempotents". Finally, it is also studied several properties relating the projective dimensions in the categories of finitely generated modules $\mathrm{mod}(U)$, $\mathrm{mod}(T)$ and $\mathrm{mod}(\Lambda ).$

References in corpus (1)

• Triangular Matrix Categories I: Dualizing Varieties and generalized one-point extension

Cited by in corpus (1)

• Triangular Matrix Categories over path Categories and Quasi-hereditary Categories, as well as one point extensions by Projectives