ICE-closed subcategories and epibricks over one-point extensions

Abstract

Let $B$ be the one-point extension algebra of $A$ by an $A$-module $M$. We proved that every ICE-closed subcategory in$\mathrm{mod}A$ can be extended to be some ICE-closed subcategories in$\mathrm{mod}B$.In the same way, every epibrick in $\mathrm{mod}A$ can be extended to be some epibricks in $\mathrm{mod}B$.The number of ICE-closed subcategories in $\mathrm{mod}B$ and the number of ICE-closed subcategories in $\mathrm{mod}A$ are denoted respectively as $m$, $n$.We can conclude the following inequality:$$m\ge 2n$$ This is the analogical in epibricks.As an application, we can get some wide $\tau$-tilting modules of $B$ by wide $\tau$-tilting modules of $A$.

10 pages