$(m,n)$-Igusa-Todorov Algebras, IT-Dimensions and Triangular Matrix Algebras
Received:July 20, 2023  Revised:December 16, 2023
Key Words: Igusa-Todorov algebras   IT-dimensions   triangular matrix algebras  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.12301041) and the Science Foundation for Distinguished Young Scholars of Anhui Province (Grant No.2108085J01).
Author NameAffiliation
Jiyuan TANG School of Mathematical Sciences, Anhui University, Anhui 230601, P. R. China 
Yuanfeng ZHANG School of Mathematical Sciences, Anhui University, Anhui 230601, P. R. China 
Hanpeng GAO School of Mathematical Sciences, Anhui University, Anhui 230601, P. R. China 
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Abstract:
      Let $T$, $U$ be two Artin algebras and $_U M_T$ be a $U$-$T$-bimodule. In this paper, we get a necessary and sufficient condition such that the formal triangular matrix algebra $\Lambda=\left({\smallmatrix T&0\\ M&U\endsmallmatrix}\right)$ is $(m,n)$-Igusa-Todorov when $_U M$, $M_T$ are projective. We also study the Igusa-Todorov dimension of $\Lambda$. More specifically, it is proved that $$\max\{\ITdim T, \ITdim U\}\leqslant\ITdim \Lambda\leqslant\min\{\max\{\gldim T,\ITdim U\},\max\{\gldim U,\ITdim T\}\}.$$
Citation:
DOI:10.3770/j.issn:2095-2651.2024.03.006
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