For a twisted partial action Θ of a group G on an (associative nonnecessarily unital) algebra A over a commutative unital ring k, the crossed product A Θ G is proved to be associative. Given a G-graded k-algebra B = g∈G B g with the mild restriction of homogeneous non-degeneracy, a criteria is established for B to be isomorphic to the crossed product B 1 Θ G for some twisted partial action of G on B 1 . The equalityis one of the ingredients of the criteria, and if it holds and, moreover, B has enough local units, then it is shown that B is stably isomorphic to a crossed product by a twisted partial action of G.

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Abstract. 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.

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Abstract. 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 FG → F n which maps G to the standard basis of F n . Many classical linear codes have been shown to be group codes. In this paper we obtain a criterion to decide when a linear code is a group code in terms of its intrinsical properties in the ambient space F n , which does not assume an "a priori" group algebra structure on F n . As an application we provide a family of groups (including metacyclic groups) for which every two-sided group code is an abelian group code.It is well known that Reed-Solomon codes are cyclic and its parity check extensions are elementary abelian group codes. These two classes of codes are included in the class of Cauchy codes. Using our criterion we classify the Cauchy codes of some lengths which are left group codes and the possible group code structures on these codes.