Geodesic
Goldie rings graded by a group with periodic quotient group modulo the center
Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 2, pp. 187-191 
A. L. Kanunnikov. Goldie rings graded by a group with periodic quotient group modulo the center. Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 2, pp. 187-191. http://geodesic.mathdoc.fr/item/FPM_2016_21_2_a7/
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     title = {Goldie rings graded by a group with periodic quotient group modulo the center},
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     url = {http://geodesic.mathdoc.fr/item/FPM_2016_21_2_a7/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we study gr-prime and gr-semiprime Goldie rings graded by a group with periodic quotient group modulo the center. We enhance the theorem of Goodearl and Stafford (2000) about gr-prime rings graded by Abelian groups; we extend the Abelian group class to the class of groups with periodic quotient group modulo the center. We also decompose the orthogonal graded completion $O^{\mathrm{gr}}(R)$ of a gr-semiprime Goldie ring $R$ (graded by a group satisfying the same condition) into a direct sum of gr-prime Goldie rings $R_1,\dots, R_n$ and prove that the maximal graded quotient ring $Q^{\mathrm{gr}}(R)$ equals the direct sum of classical graded quotients rings of $R_1,\dots, R_n$.

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