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1
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Strongly groupoid graded rings and cohomology

100%
Lundström P.
Colloquium Mathematicum
|
2006
|
tom 106
|
nr 1
1-13
EN
We interpret the collection of invertible bimodules as a groupoid and call it the Picard groupoid. We use this groupoid to generalize the classical construction of crossed products to what we call groupoid crossed products, and show that these coincide with the class of strongly groupoid graded rings. We then use groupoid crossed products to obtain a generalization from the group graded situation to the groupoid graded case of the bijection from a second cohomology group, defined by the grading and the functor from the groupoid in question to the Picard groupoid, to the collection of equivalence classes of rings strongly graded by the groupoid.
2
Content available remote

Normal bases for infinite Galois ring extensions

100%
Lundström P.
Colloquium Mathematicum
|
1999
|
tom 79
|
nr 2
235-240
3
Content available remote

Normal integral bases for infinite abelian extensions

100%
Lundström P.
Acta Arithmetica
|
2001
|
tom 100
|
nr 1
79-83
4
Content available remote

Self-dual normal bases for infinite odd abelian Galois ring extensions

100%
Lundström P.
Acta Arithmetica
|
2006
|
tom 123
|
nr 1
1-8
5
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The category of groupoid graded modules

100%
Lundström P.
Colloquium Mathematicum
|
2004
|
tom 100
|
nr 2
195-211
EN
We introduce the abelian category R-gr of groupoid graded modules and give an answer to the following general question: If U: R-gr → R-mod denotes the functor which associates to any graded left R-module M the underlying ungraded structure U(M), when does either of the following two implications hold: (I) M has property X ⇒ U(M) has property X; (II) U(M) has property X ⇒ M has property X? We treat the cases when X is one of the properties: direct summand, free, finitely generated, finitely presented, projective, injective, essential, small, and flat. We also investigate when exact sequences are pure in R-gr. Some relevant counterexamples are indicated.
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