Graded Versions of Goldie's Theorem / Kanunnikov A.L. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2011. № 3. P. 46-50 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].
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 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.
graded Goldie's rings, graded quotient rings.