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Chain conditions for Leavitt path algebras
Abstract In this paper we give necessary and sufficient conditions on a row-finite graph E so that the corresponding (not necessarily unital) Leavitt path K-algebra LK (E) is either artinian orExpand
Algebras of quotients of Lie algebras
In this paper we introduce the notion of algebra of quotients of a Lie algebra. Properties such as semiprimeness, primeness or nondegeneracy can be lifted from a Lie algebra to its algebras ofExpand
Evolution algebras of arbitrary dimension and their decompositions
We study evolution algebras of arbitrary dimension. We analyze in deep the notions of evolution subalgebras, ideals and non-degeneracy and describe the ideals generated by one element andExpand
The socle of a Leavitt path algebra
In this paper we characterize the minimal left ideals of a Leavitt path algebra as those which are isomorphic to principal left ideals generated by line points; that is, by vertices whose treesExpand
Left Quotient Associative Pairs and Morita Invariant Properties
In this paper, we prove that left nonsingularity and left nonsingularity plus finite left local Goldie dimension are two Morita invariant properties for idempotent rings without total left or rightExpand
Long-term follow-up of asymptomatic HIV-infected patients who discontinued antiretroviral therapy.
BACKGROUND Whether asymptomatic human immunodeficiency virus (HIV)-infected patients can interrupt treatment remains unknown. METHODS We performed a prospective, observational study of 46 patientsExpand
Finite-dimensional Leavitt path algebras
Abstract We classify the directed graphs E for which the Leavitt path algebra L ( E ) is finite dimensional. In our main results we provide two distinct classes of connected graphs from which, moduloExpand
Socle theory for Leavitt path algebras of arbitrary graphs
The main aim of the paper is to give a socle theory for Leavitt path algebras of arbitrary graphs. We use both the desingularization process and combinatorial methods to study Morita invariantExpand
Graph C∗-Algebras, and Their Relationship to Leavitt Path Algebras
In this chapter we investigate the connections between Leavitt path algebras (with coefficients in \(\mathbb{C}\)), and their analytic counterparts, the graph C ∗-algebras. We start by giving a briefExpand
Associative and Lie algebras of quotients
In this paper we examine how the notion of algebra of quotients for Lie algebras ties up with the corresponding well-known concept in the associative case. Specifically, we completely characterizeExpand