Geodesic
Graded rings with finiteness conditions
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 3, pp. 23-35
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This paper is devoted to quotient rings of graded rings with finiteness conditions for ideals. The analogs of Goldie, Shock, and Small theorems are proved. We find criteria for a graded ring $R$ to admit a gr-semisimple and gr-Artinian (the Goldie theorem) and gr-Artinian (the Small theorem) classical graded quotient ring. 
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D. S. Bazhenov; A. L. Kanunnikov. Graded rings with finiteness conditions. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 3, pp. 23-35. http://geodesic.mathdoc.fr/item/FPM_2020_23_3_a2/

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