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  • 1.
    Lundström, Patrik
    University West, Department of Technology.
    Normal Bases for Infinite Galois Ring Extensions1999In: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 79, p. 235-240Article in journal (Refereed)
  • 2.
    Lundström, Patrik
    University West, Department of Technology, Mathematics and Computer Science.
    The category of groupoid graded modules2004In: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 100, p. 15p. 195-211Article in journal (Refereed)
  • 3.
    Lundström, Patrik
    University West, Department of Technology, Mathematics and Computer Science.
    The Picard Groupoid and Strongly Groupoid Graded Modules2006In: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 106, p. 1-13Article in journal (Refereed)
  • 4.
    Lundström, Patrik
    University West, Department of Engineering Science.
    The Picard Groupoid and Strongly Groupoid Graded Modules2006In: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 106, p. 1-13Article in journal (Refereed)
  • 5.
    Lundström, Patrik
    et al.
    University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.
    Öinert, Johan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences, Karlskrona (SWE).
    Richter, Johan
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences, Karlskrona (SWE).
    Non-Unital Ore Extensions2023In: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 172, no 2, p. 217-229Article in journal (Refereed)
    Abstract [en]

    We study Ore extensions of non-unital associative rings. We provide a characterization of simple non-unital differential polynomial rings R[x; delta], under the hy-pothesis that R is s-unital and ker(delta) contains a non-zero idempotent. This result gener-alizes a result by oinert, Richter and Silvestrov from the unital setting. We also present a family of examples of simple non-unital differential polynomial rings.

  • 6.
    Nystedt, Patrik
    University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.
    Simplicity of algebras via epsilon-strong systems2020In: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 162, no 2, p. 279-301Article in journal (Refereed)
    Abstract [en]

    We obtain sufficient criteria for simplicity of systems, that is, rings R that are equipped with a family of additive subgroups R-s for s is an element of S, where S is a semigroup satisfying R = Sigma (s is an element of S) R-s and RsRt subset of R-st for s, t is an element of S. These criteria are specialized to obtain sufficient criteria for simplicity of what we call s-unital epsilon-strong systems, that is, systems where S is an inverse semigroup, R is coherent, in the sense that R-s subset of R-t for all s, t is an element of S with s <= t and for each s is an element of S, the RsRs*-Rs*Rs -bimodule R-s is s-unital. As an application, we obtain generalizations of recent criteria for simplicity of skew inverse semigroup rings by Beuter, Goncalves, Oinert and Royer, and then for Steinberg algebras over non-commutative rings by Brown, Farthing, Sims, Steinberg, Clark and Edie-Michell.

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