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Graded rings and equivalences of categories. (English) Zbl 0722.16020

Let \(R\) and \(A\) be graded rings (not necessarily over the same group). The paper studies the following problem: When the categories \(R\)-gr and \(A\)-gr are equivalent? The answer is given in terms of certain \(R\)-\(A\)-bimodules. Several applications are given.

MSC:

16W50 Graded rings and modules (associative rings and algebras)
16D90 Module categories in associative algebras
16D20 Bimodules in associative algebras
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References:

[1] Gordon R., J. of Algebra 76 pp 241– (1980)
[2] Hilton P.J., A Course in Homological Algebra (1971)
[3] DOI: 10.1016/0022-4049(88)90067-9 · Zbl 0657.16025
[4] Montgomery, S. Fixed Rings of Finite Automorphism Groups of Associative Rings. Lect. Notes in Math. Vol. 818, Berlin: Springer. · Zbl 0449.16001
[5] DOI: 10.1016/0021-8693(89)90192-0 · Zbl 0678.16001
[6] Năstaăsescu, C. 1980. Graded Ring Theory. Conference. 1980, North–Holland, Amsterdam. Mathematical Library
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