Simple flat Leavitt path algebras are von Neumann regular
نویسندگان
چکیده
منابع مشابه
Weakly Noetherian Leavitt Path Algebras
We study row-finite Leavitt path algebras. We characterize the row-finite graphs E for which the Leavitt path algebra is weakly Noetherian. Our main result is that a Leavitt path algebra is weakly Noetherian if and only if there is ascending chain condition on the hereditary and saturated closures of the subsets of the vertices of the graph E.
متن کاملThe Matrix Type of Purely Infinite Simple Leavitt Path Algebras
Let R denote the purely infinite simple unital Leavitt path algebra L(E). We completely determine the pairs of positive integers (c, d) for which there is an isomorphism of matrix rings Mc(R) ∼= Md(R), in terms of the order of [1R] in the Grothendieck group K0(R). For a row-finite directed graph E and field k, the Leavitt path algebra Lk(E) has been defined in [1] and [9], and further investiga...
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We start this paper by showing that the Leavitt path algebra of a (row-finite) graph is an algebra of quotients of the corresponding path algebra. The path algebra is semiprime if and only if whenever there is a path connecting two vertices, there is another one in the opposite direction. Semiprimeness is studied because, for acyclic graphs, the Leavitt path algebra is a Fountain-Gould algebra ...
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متن کاملChain Conditions for Leavitt Path Algebras
In this paper, results known about the artinian and noetherian conditions for the Leavitt path algebras of graphs with finitely many vertices are extended to all row-finite graphs. In our first main result, necessary and sufficient conditions on a row-finite graph E are given so that the corresponding (not necessarily unital) Leavitt path K-algebra L(E) is semisimple. These are precisely the al...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2019
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2018.1513015