Additive closed symmetric monoidal structures on R-modules
Hovey, Mark
arXiv, 0906.1125 / Harvested from arXiv
Text on arXiv
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 Lambda_{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 monoidal structures on R-modules, for which there is exactly one (up to isomorphism), for which there are exactly seven, and for which there are a proper class of isomorphism classes of such structures. We also prove some general structual results; for example, we prove that the unit K must always be a finitely generated R-module.
Publié le : 2009-06-05
Classification:  Mathematics - Category Theory,  Mathematics - Rings and Algebras,  18D10,  16D90 
@article{0906.1125,
     author = {Hovey, Mark},
     title = {Additive closed symmetric monoidal structures on R-modules},
     journal = {arXiv},
     volume = {2009},
     number = {0},
     year = {2009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0906.1125}
}

Hovey, Mark. Additive closed symmetric monoidal structures on R-modules. arXiv, Tome 2009 (2009) no. 0, . http://gdmltest.u-ga.fr/item/0906.1125/