Juan Jacobo Simón

Morita equivalence for idempotent rings

Abstract In this paper, the classical theory of Morita equivalence is extended to idempotent rings which do not necessarily have an identity element. In this case, the role of progenerators is played by the unital and codivisible modules which generate all the unital modules.

On Monomial Characters and Central Idempotents of Rational Group Algebras

Abstract We give a method to obtain the primitive central idempotent of the rational group algebra ℚG over a finite group G associated to a monomial irreducible character which does not involve computations with the character field nor its Galois group. We also show that for abelian-by-supersolvable groups this method takes a particularly easy form that can be used to compute the Wedderburn decomposition of ℚG.

Globalization of twisted partial actions

Let A be a unital ring which is a product of possibly infinitely many indecomposable rings. We establish a criteria for the existence of a globalization for a given twisted partial action of a group on A. If the globalization exists, it is unique up to a certain equivalence relation and, moreover, the crossed product corresponding to the twisted partial action is Morita equivalent to that corresponding to its globalization. For arbitrary unital rings the globalization problem is reduced to an extendibility property of the multipliers involved in the twisted partial action.

Globalizations of partial actions on nonunital rings

In this note we prove a criteria for the existence of a globalization for a given partial action of a group on an s-unital ring. If the globalization exists, it is unique in a natural sense. This extends the globalization theorem from Dokuchaev and Exel, 2005, obtained in the context of rings with 1.

The Group of Automorphisms of the Rational Group Algebra of a Finite Metacyclic Group

We investigate the group of automorphisms Aut(ℚ G) of a rational group algebra ℚ G of a finite metacyclic group G by first describing the simple components of the Wedderburn decomposition of ℚ G and then investigating when two of these simple components are isomorphic.

An intrinsical description of group codes

A (left) group code of length n is a linear code which is the image of a (left) ideal of a group algebra via an isomorphism

Information Sets From Defining Sets in Abelian Codes

{\mathbb{F}G \rightarrow \mathbb{F}^n}

Isomorphisms of Partial Group Rings

which maps G to the standard basis of