Antonio Paques

TL;DR: In this article, a Galois theory of commutative rings under partial actions of finite groups was developed, extending the well-known results by S.U. Chase, D.K.Harrison and A.Rosenberg.

TL;DR: In this paper, the authors introduce the notion of a partial action of a groupoid on a ring as well as a criteria for the existence of a globalization of it, and construct a Morita context associated to a globalizable partial groupoid action.

Abstract: In this paper, we introduce the notion of a partial action of an ordered groupoid on a ring and we construct the corresponding partial skew groupoid ring. We present sufficient conditions under which the partial skew groupoid ring is either associative or unital. Also, we show that there is a one-to-one correspondence between partial actions of an ordered groupoid G on a ring R, in which the domain of each partial bijection is an ideal, and meet-preserving global actions of the Birget–Rhodes expansion GBR of G on R. Using this correspondence, we prove that the partial skew groupoid ring is a homomorphic image of the skew groupoid ring constructed through the Birget–Rhodes expansion.

TL;DR: In this article, the primitive central idempotents of a rational group algebra of a finite nilpotent group are described, which does not make use of the character table of the group G.

TL;DR: In this paper, the crossed product S = R⋆α G by a twisted partial action α of a group G on a ring R was studied and necessary and sufficient conditions for S to be a separable (resp., Frobenius, semisimple) extension of R.