Enrique Pardo

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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)
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)
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)
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)
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)