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$\mod A$ can be extended to be some ICE-closed subcategories in$\mod B$.In the same way, every epibrick in $\mod A$ can be extended to be some epibricks in $\mod B$.The number of ICE-closed subcategories in $\mod B$ and the number of ICE-closed subcategories in $\mod A$ are denoted respectively as $m$, $n$.We can conclude the following inequality:$$m \geq 2n$$ This is the analogical in epibricks.As an application, we can get some wide $τ$-tilting modules of $B$ by wide $τ$-tilting modules of $A$.

Theorems & Definitions (17)

• Theorem 1.1
• Theorem 1.2
• Definition 2.1
• Definition 2.2
• Corollary 2.3
• Definition 2.4
• Theorem 3.1
• Example 3.2
• Remark 3.3
• Corollary 3.4