Partial generalized crossed products and a seven-term exact sequence - ScienceDirect Skip
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Let G be a group, let A=⊕ g∈ GA g be an epsilon-strongly graded ring over G, let R:= A 1 be
the homogeneous component associated with the identity of G, and let 𝙿𝚒𝚌𝚂⁢(R) be the …

Let R be a ring with a set of local units, and a homomorphism of groups Θ̲: G→ Pic (R) to
the Picard group of R. We study under which conditions Θ̲ is determined by a factor map …

Given a unital partial representation Θ of a group G into the Picard semigroup PicS (R), we
construct an abelian group C (Θ/R) formed by the isomorphism classes of generalized …

Given a non-necessarily commutative unital ring $ R $ and a unital partial representation
$\Theta $ of a group $ G $ into the Picard semigroup $\mathbf {PicS}(R) $ of the …

We prove that the classical result asserting that the relative Picard group of a faithfully flat
extension of commutative rings is isomorphic to the first Amitsur cohomology group still is …

Given a non-necessarily commutative unital ring R and a unital partial representation Θ of a
group G into the Picard semigroup PicS (R) of the isomorphism classes of partially invertible …

Para uma extensão de Galois de anéis comutativos, Chase-Harrison-Rosenberg
construíram uma sequência exata de sete termos que envolve o grupo de Picard, o grupo …