AI 中文总结
研究关联代数的砖块连续性与通用砖块，先证十二个最小表示无限关联代数族的情况，再通过逆转偏序集约化过程推广到任意表示无限关联代数，还给出应用这些结果到更广泛代数类的方法。
AI 中文摘要
我们将证明，十二个最小表示无限关联代数族是砖块连续的，并承认一个通用砖块，该通用砖块将被明确构造。之后，通过逆转偏序集之间的约化过程，我们将证明任何表示无限关联代数都是砖块连续的，并承认一个通用砖块，该通用砖块可以使用所谓的“扩展函子”明确计算。最后，给出了一种将这些结果应用于更广泛代数类的方法。
英文摘要
We will show that the twelve families of minimally representation-infinite incidence algebras are brick-continuous and admit a generic brick, which will be explicitly constructed. After that, reversing the reduction process between posets, we will show that any representation-infinite incidence algebra is brick-continuous and admits a generic brick, which can be explicitly computed using what will be called ``extension functors''. Lastly, a method to apply these results to a broader class of algebras is given.
Comments20 pages
