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  • 1.
    Nystedt, Patrik
    University West, Department of Engineering Science, Division of Natural Sciences and Electrical and Surveying Engineering.
    A combinatorial proof of associativity of Ore extensions2013In: Discrete Mathematics, ISSN 0012-365X, E-ISSN 1872-681X, Vol. 313, no 23, p. 2748-2750Article in journal (Refereed)
    Abstract [en]

    We use a counting argument to show that Ore extensions are associative. 

  • 2.
    Nystedt, Patrik
    et al.
    University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.
    Öinert, Johan
    Blekinge Inst Technol, Dept Math & Nat Sci, SE-37179 Karlskrona, Sweden.
    Pinedo, Hector
    Univ Ind Santander, Escuela Matemat, Carrera 27 Calle 9, Bucaramanga, Colombia (COL).
    Epsilon-Strongly Groupoid-Graded Rings, The Picard Inverse Category And Cohomology2020In: Glasgow Mathematical Journal, ISSN 0017-0895, E-ISSN 1469-509X, Vol. 62, no 1, p. 233-259Article in journal (Refereed)
    Abstract [en]

    We introduce the class of partially invertible modules and show that it is an inverse category which we call the Picard inverse category. We use this category to generalize the classical construction of crossed products to, what we call, generalized epsilon-crossed products and show that these coincide with the class of epsilon-strongly groupoid-graded rings. We then use generalized epsilon-crossed groupoid products to obtain a generalization, from the group-graded situation to the groupoid-graded case, of the bijection from a certain second cohomology group, defined by the grading and the functor from the groupoid in question to the Picard inverse category, to the collection of equivalence classes of rings epsilon-strongly graded by the groupoid.

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