论文标题
独立代数范围限制范围的内态半群
The semigroup of endomorphisms with restricted range of an independence algebra
论文作者
论文摘要
自西蒙斯（Symons）引入以来，在集合上的转换或向量空间上的线性地图的背景下研究了具有限制范围的地图的半群。集合和矢量空间是独立代数的特定示例，一个自然的问题是，是否要摄取所有内态的所有内态的semigroup $ t（\ nathcal {a}，\ nathcal {b}）$的独立性代数$ \ nmathcal {a} $ sy subalgebra $ cains can beccalbra $ \ supcc cains的所有内态的$ \ supccals in subalgebra a}集合和向量空间的情况。在本文中，我们将Sanwong，Sommanee，Sullivan，Mendes-Gonçalves及其所有前辈的研究置于一个共同的框架之下。我们描述了Green的关系以及$ T（\ Mathcal {a}，\ Mathcal {B}）$的理想。然后，我们迈出了一个新的方向，完全描述了$ t（\ Mathcal {a}，\ Mathcal {b}）$上的所有扩展绿色关系。我们对代数的维度没有限制，因为有限和无限尺寸案例的结果通常采用相同的形式。
Since its introduction by Symons, the semigroup of maps with restricted range has been studied in the context of transformations on a set, or of linear maps on a vector space. Sets and vector spaces being particular examples of independence algebras, a natural question that arises is whether by taking the semigroup $T(\mathcal{A},\mathcal{B})$ of all endomorphisms of an independence algebra $\mathcal{A}$ whose image lie in a subalgebra $\mathcal{B}$, one can obtain corresponding results as in the cases of sets and vector spaces. In this paper, we put under a common framework the research from Sanwong, Sommanee, Sullivan, Mendes-Gonçalves and all their predecessors. We describe Green's relations as well as the ideals of $T(\mathcal{A},\mathcal{B})$ following their lead. We then take a new direction, completely describing all of the extended Green's relations on $T(\mathcal{A},\mathcal{B})$. We make no restriction on the dimension of our algebras as the results in the finite and infinite dimensional cases generally take the same form.
