The dual ring to a coring with a grouplike

Kleiner, Mark

doi:10.1090/S0002-9939-1984-0746085-5

The dual ring to a coring with a grouplike
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Proc. Amer. Math. Soc. 91 (1984), 540-542 Request permission

Abstract:

A matrix problem is that of the classification up to isomorphism of induced comodules over a coring with a grouplike. To define such a problem, using a more familiar language of induced modules, one wants to know what ring is dual to a coring with a grouplike. The answer is given in this paper.

References

Maurice Auslander, Representation theory of Artin algebras. I, II, Comm. Algebra 1 (1974), 177–268; ibid. 1 (1974), 269–310. MR 349747, DOI 10.1080/00927877408548230
Maurice Auslander and Idun Reiten, Representation theory of Artin algebras. III. Almost split sequences, Comm. Algebra 3 (1975), 239–294. MR 379599, DOI 10.1080/00927877508822046
Henri Cartan and Samuel Eilenberg, Homological algebra, Princeton University Press, Princeton, N. J., 1956. MR 0077480
Mark Kleiner, Induced modules and comodules and representations of BOCSs and DGCs, Representations of algebras (Puebla, 1980) Lecture Notes in Math., vol. 903, Springer, Berlin-New York, 1981, pp. 168–185. MR 654709
M. M. Kleĭner and A. V. Roĭter, Representations of differential graded categories, Matrix problems (Russian), Akad. Nauk Ukrain. SSR Inst. Mat., Kiev, 1977, pp. 5–70 (Russian). MR 0573937
A. V. Rojter, Matrix problems and representations of BOCSs, Representation theory, I (Proc. Workshop, Carleton Univ., Ottawa, Ont., 1979), Lecture Notes in Math., vol. 831, Springer, Berlin-New York, 1980, pp. 288–324. MR 607144
A. V. Roĭter and M. M. Kleiner, Representations of differential graded categories, Representations of algebras (Proc. Internat. Conf., Carleton Univ., Ottawa, Ont., 1974) Lecture Notes in Math., Vol. 488, Springer, Berlin, 1975, pp. 316–339. MR 0435145
Moss Sweedler, The predual theorem to the Jacobson-Bourbaki theorem, Trans. Amer. Math. Soc. 213 (1975), 391–406. MR 387345, DOI 10.1090/S0002-9947-1975-0387345-9