Principally-Injective Leavitt Path Algebras over Arbitrary Graphs

• 作者: Ardeline M.Buhphang Soumitra Das
• 来源期刊: 数学和系统科学:英文版
• 学科: 数学
• 关键词: Leavitt path ALGEBRAS von NEUMANN regular RINGS principally-injective RINGS ARBITRARY graph
• 年，卷（期）: 2019,（3）
• 页码范围: 86-89
• 页数: 4页
• 分类号: O1

摘要

ring R is called right principally-injective if every R-homomorphism f:aR→R,a∈R,extends to R,or equivalently,if every system of equations xa=b(a,b∈R)is solvable in R.In this paper we show that for any arbitrary graph E and for a field K,principally-injective conditions for the Leavitt path algebra LK(E)are equivalent to that graph E being acyclic.We also show that the principally-injective Leavitt path algebras are precisely the von Neumann regular Leavitt path algebras.