Geodesic
Graded versions of Goldie's theorem
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2011), pp. 46-50

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We prove the graded variants of Goldie's theorem of existence, structure and coincidence of right classical and maximal quotient rings of a semiprime (prime) right Goldie's ring (Theorems 10, 11, 13). The main problem, the existence of a homogeneous regular element in each $\operatorname{gr}$-essential right ideal, is solved by posing some additional requirements onto the group grading the ring or onto the homogeneous components of the ring. 
@article{VMUMM_2011_3_a9,
     author = {A. L. Kanunnikov},
     title = {Graded versions of {Goldie's} theorem},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {46--50},
     publisher = {mathdoc},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2011_3_a9/}
}
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A. L. Kanunnikov. Graded versions of Goldie's theorem. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2011), pp. 46-50. http://geodesic.mathdoc.fr/item/VMUMM_2011_3_a9/