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Pentagonal Relations and the Exchange Module of the Type $A_n$ Cluster Algebra
Associahedron Cluster Algebra Discrete Homotopy Theory
2011/1/21
In this paper we study relations between the exchange relations in the cluster algebra of type-An, which has the 1-skeleton of the associahedron as its exchange graph, and the complex of triangulation...
Exchange rings generated by their units
置换环 本原分式环 强$\pi$正则环
2007/12/10
假设$R$为本原分式Artinian环,证明了有$u\in U(R)$使得$1_R\pm u\in U(R)$ 当且仅当对任何$a\in R$, 有$u\in U(R)$使得$a\pm u\in U(R)$. 进一步，证明了 对任何$A\in M_n(R)(n\geq 2)$, 有$U\in GL_n(R)$ 使得$A\pm U\in GL_n(R)$. 作为应用得到了强$\pi$正则环中任何元素...