# A note on the regular ideals of Leavitt path algebras

@article{Gonccalves2021ANO, title={A note on the regular ideals of Leavitt path algebras}, author={Daniel Gonccalves and Danilo Royer}, journal={Journal of Algebra and Its Applications}, year={2021} }

We show that, for an arbitrary graph, a regular ideal of the associated Leavitt path algebra is also graded. As a consequence, for a row-finite graph, we obtain that the quotient of the associated Leavitt path by a regular ideal is again a Leavitt path algebra and that Condition (L) is preserved by quotients by regular ideals. Furthermore, we describe the vertex set of a regular ideal and make a comparison between the theory of regular ideals in Leavitt path algebras and in graph C*-algebras.

## 4 Citations

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## References

SHOWING 1-10 OF 27 REFERENCES

Using the Steinberg algebra model to determine the center of any Leavitt path algebra

- MathematicsIsrael Journal of Mathematics
- 2019

Given an arbitrary graph, we describe the center of its Leavitt path algebra over a commutative unital ring. Our proof uses the Steinberg algebra model of the Leavitt path algebra. A key ingredient…

Regular ideals of graph algebras

- MathematicsRocky Mountain Journal of Mathematics
- 2022

Let $C^*(E)$ be the graph C$^*$-algebra of a row-finite graph $E$. We give a complete description of the vertex sets of the gauge-invariant regular ideals of $C^*(E)$. It is shown that when $E$…

On Generators of Two-Sided Ideals of Leavitt Path Algebras over Arbitrary Graphs

- Mathematics
- 2014

Let E be an arbitrary graph and K be any field. For any nongraded ideal I of the Leavitt path algebra L K (E), we give an explicit description of a set of generators of I. This leads to a number of…

Leavitt Path Algebras

- Mathematics
- 2017

The central concept of this thesis is that of Leavitt path algebras, a notion introduced by both Abrams and Aranda Pino in [AA1] and Ara, Moreno and Pardo in [AMP] in 2004. The idea of using a field…

The Groupoid Approach to Leavitt Path Algebras

- MathematicsLeavitt Path Algebras and Classical K-Theory
- 2020

When the theory of Leavitt path algebras was already quite advanced, it was discovered that some of the more difficult questions were susceptible to a new approach using topological groupoids. The…

Strongly graded groupoids and strongly graded Steinberg algebras

- MathematicsJournal of Algebra
- 2019

Structure theory of graded regular graded
self-injective rings and applications

- MathematicsCategorical, Homological and Combinatorial Methods in Algebra
- 2020

In this paper, we develop structure theory for graded regular graded self-injective rings and apply it in the context of Leavitt path algebras. We show that for a finite graph, graded regular graded…

Representations of relative Cohn path algebras

- MathematicsJournal of Pure and Applied Algebra
- 2020

Existence of maximal ideals in Leavitt path algebras

- MathematicsTURKISH JOURNAL OF MATHEMATICS
- 2018

Let E be an arbitrary directed graph and let L be the Leavitt path algebra of the graph E over a field K. The necessary and sufficient conditions are given to assure the existence of a maximal ideal…