论文标题
线性地图保存产品等于发射率的原始构素
Linear maps preserving products equal to primitive idempotents of an incidence algebra
论文作者
论文摘要
令$ a $，$ b $为代数和$ a \ in $，$ b \ in b $ in固定的元素。我们说，如果所有$ a_1，a_2 \ in $ equality $ a_1a_2 = a $ nime $ umimimimφ（a_1）φ（a_2）φ（a_2）= b $。在本文中，我们研究了b biontive线性地图$φ：i（x，f）\ to i（x，x，f）$保留产品，等于$ i（x，f）$的原始idempotents，其中$ i（x，f）$是有限连接的poset $ x $ x $ x $ field $ f $ by field $ f $的发生率代数。我们完全表征了这种情况，当存在这样的地图$φ$时，$φ$要么是$ i（x，f）$的自动形态，要么是$ i（x，f）$的自动形态的否定。
Let $A$, $B$ be algebras and $a\in A$, $b\in B$ a fixed pair of elements. We say that a map $φ:A\to B$ preserves products equal to $a$ and $b$ if for all $a_1,a_2\in A$ the equality $a_1a_2=a$ implies $φ(a_1)φ(a_2)=b$. In this paper we study bijective linear maps $φ:I(X,F)\to I(X,F)$ preserving products equal to primitive idempotents of $I(X,F)$, where $I(X,F)$ is the incidence algebra of a finite connected poset $X$ over a field $F$. We fully characterize the situation, when such a map $φ$ exists, and whenever it does, $φ$ is either an automorphism of $I(X,F)$ or the negative of an automorphism of $I(X,F)$.
