论文标题
代数的换向率支架
Commutativity preservers of incidence algebras
论文作者
论文摘要
令$ i（x，k）$为有限连接的poset $ x $在field $ k $和$ d（x，k）$的发病率代数，其subalgebra由对角线元素组成。我们描述了b biote -linear maps $φ：i（x，k）\ to i（x，k）$，强烈保留通勤性并满足$φ（d（x，k））= d（x，x，k）$。我们证明，这样的映射$φ$是转换类型的通勤性保存器的组成，是与四倍的$（θ，σ，c，κ）$ simply Maps $θ$，$σ$，$σ$，$ c $和$ k $ elements的序列$κ$κ$κ$ k $相关的交换性保存器。
Let $I(X,K)$ be the incidence algebra of a finite connected poset $X$ over a field $K$ and $D(X,K)$ its subalgebra consisting of diagonal elements. We describe the bijective linear maps $φ:I(X,K)\to I(X,K)$ that strongly preserve the commutativity and satisfy $φ(D(X,K))=D(X,K)$. We prove that such a map $φ$ is a composition of a commutativity preserver of shift type and a commutativity preserver associated to a quadruple $(θ,σ,c,κ)$ of simpler maps $θ$, $σ$, $c$ and a sequence $κ$ of elements of $K$.
