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Quotients of Leavitt path algebras over rings by $I$-basic graded ideals

Sevgi Harman, Müge Kanuni, Guillermo Vera de Salas

Abstract

In this paper, the quotient of a Leavitt path algebra of an arbitrary graph by an $I$-basic graded ideal, and the quotient of a Leavitt path algebra of a row-finite graph by an arbitrary graded ideal are considered. The result of the quotient of a Leavitt path algebra by an arbitrary graded ideal is extended by using the function $\varphi$. Examples are given to illustrate the results.

Quotients of Leavitt path algebras over rings by $I$-basic graded ideals

Abstract

In this paper, the quotient of a Leavitt path algebra of an arbitrary graph by an -basic graded ideal, and the quotient of a Leavitt path algebra of a row-finite graph by an arbitrary graded ideal are considered. The result of the quotient of a Leavitt path algebra by an arbitrary graded ideal is extended by using the function . Examples are given to illustrate the results.
Paper Structure (12 sections, 14 theorems, 55 equations)

This paper contains 12 sections, 14 theorems, 55 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Leavitt path algebras
  4. Lattices required within the text
  5. Basic Ideals / Graded Ideals
  6. Arbitrary ideals in Leavitt path algebras
  7. Condition (K) iff all ideals are graded ideals
  8. Graph Constructions
  9. Main Theorems
  10. Quotient of a Leavitt path algebra by an $I$-basic graded ideal
  11. Graded ideal function
  12. Quotient of a Leavitt path algebra via a graded ideal function

Key Result

Corollary 2.5

There is a lattice isomorphism $\mathcal{L}_{gr}(L_R(E)) \rightarrow \mathcal{F}_{E,R}$ that sends a graded ideal $A$ to $f$, with The inverse of this map is given by

Theorems & Definitions (41)

  • Definition 2.1
  • Definition 2.2
  • Example 2.3
  • Definition 2.4
  • Corollary 2.5
  • Remark 2.6
  • Remark 2.7
  • Lemma 2.8
  • Proposition 2.9
  • proof
  • ...and 31 more