## 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

### Keywords:

equivalences of categories; graded rings; bimodules
Full Text:

### 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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