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- P Ara, M A Moreno, E Pardo
- 2008

We compute the monoid V (LK(E)) of isomorphism classes of finitely generated projective modules over certain graph algebras LK(E), and we show that this monoid satisfies the refinement property and separative cancellation. We also show that there is a natural isomorphism between the lattice of graded ideals of LK(E) and the lattice of order-ideals of V… (More)

We prove an algebraic version of the Gauge-Invariant Uniqueness Theorem, a result which gives information about the injectivity of certain homomorphisms between Zgraded algebras. As our main application of this theorem, we obtain isomorphisms between the Leavitt path algebras of specified graphs. From these isomorphisms we are able to achieve two ends.… (More)

- Friedrich Wehrung, Ken Goodearl, Enrique Pardo
- 2008

We characterize, in terms of elementary properties, the abelian monoids which are direct limits of finite direct sums of monoids of the form (Z/nZ)⊔{0} (where 0 is a new zero element), for positive integers n. The key properties are the Riesz refinement property and the requirement that each element x has finite order, that is, (n + 1)x = x for some… (More)

- P Ara, K R Goodearl, E Pardo
- 2008

We extend the notion of a purely infinite simple C*-algebra to the context of unital rings, and we study its basic properties, specially those related to K-Theory. For instance, if R is a purely infinite simple ring, then K0(R) + = K0(R), the monoid of isomorphism classes of finitely generated projective R-modules is isomorphic to the monoid obtained from… (More)

- G Aranda Pino, E Pardo, M Siles Molina
- 2008

We characterize Leavitt path algebras which are exchange rings in terms of intrinsic properties of the graph and show that the values of the stable rank for these algebras are 1, 2 or ∞. Concrete criteria in terms of properties of the underlying graph are given for each case.

- P Ara, M A Gonz´alez-Barroso, K R Goodearl, E Pardo
- 2008

Given an action α of a monoid T on a ring A by ring endomorphisms, and an Ore subset S of T , a general construction of a fractional skew monoid ring S ∗α A ∗α T is given, extending the usual constructions of skew group rings and of skew semigroup rings. In case S is a subsemigroup of a group G such that G = SS, we obtain a G-graded ring S ∗α A ∗α S with… (More)

Abstract. Let K be any field, let Ln denote the Leavitt algebra of type (1, n − 1) having coefficients in K, and let Md(Ln) denote the ring of d × d matrices over Ln. In our main result, we show that Md(Ln) ∼= Ln if and only if d and n − 1 are coprime. We use this isomorphism to answer a question posed in [14] regarding isomorphisms between various… (More)

We give a characterization of finiteness of projections in the multiplier algebra of a σ-unital C∗-algebra of real rank zero and stable rank one.

- G Aranda Pino, E Pardo, M Siles Molina
- 2008

In this paper a bijection between the set of prime ideals of a Leavitt path algebra LK(E) and a certain set which involves maximal tails in E and the prime spectrum of K[x, x] is established. Necessary and sufficient conditions on the graph E so that the Leavitt path algebra LK(E) is primitive are also found.

- E. Pardo
- 2014

In this paper we answer Open Problem 2 of Goodearl’s book on partially ordered abelian groups in the case of partially ordered simple groups. As a consequence, we obtain a version of the Theorem of structure of dimension groups in the case of simple Riesz groups. Also, we give a method for constructing torsion-free strictly perforated simple Riesz groups of… (More)