Additive closed symmetric monoidal structures on R-modules

@article{Hovey2009AdditiveCS,
  title={Additive closed symmetric monoidal structures on R-modules},
  author={M. Hovey},
  journal={Journal of Pure and Applied Algebra},
  year={2009},
  volume={215},
  pages={789-805}
}
  • M. Hovey
  • Published 2009
  • Mathematics
  • Journal of Pure and Applied Algebra
  • Abstract In this paper, we classify additive closed symmetric monoidal structures on the category of left R -modules by using Watts’ theorem. An additive closed symmetric monoidal structure is equivalent to an R -module Λ A , B equipped with two commuting right R -module structures represented by the symbols A and B , an R -module K to serve as the unit, and certain isomorphisms. We use this result to look at simple cases. We find rings R for which there are no additive closed symmetric… CONTINUE READING
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    Homotopy Theory of linear cogebras
    • 7
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    References

    SHOWING 1-10 OF 21 REFERENCES
    Intrinsic characterizations of some additive functors
    • 130
    • PDF
    On commutative endomorphism rings.
    • 9
    • Highly Influential
    • PDF
    Intersection homological algebra
    • 11
    • PDF
    On braided tensor categories
    • 238
    • PDF
    A first course in noncommutative rings
    • T. Lam
    • Mathematics, Physics
    • 1991
    • 1,403
    Lectures on modules and rings
    • 1,140
    Graduate Texts in Mathematics
    • 8,057
    Intersection homological algebra, New topological contexts for Galois theory and algebraic geometry (BIRS
    • Geom. Topol. Monogr.,
    • 2008
    Mark Hovey, Intersection homological algebra, to appear
    • Mark Hovey, Intersection homological algebra, to appear
    • 2008
    18009 ) [ Hov 08 ] Mark Hovey , Intersection homological algebra , to appear , 2008 . [ JS 93 ] André Joyal and Ross Street , Braided tensor categories
    • Adv . Math . Lectures on modules and rings , Graduate Texts in Mathematics
    • 1999