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Graded versions of Goldie's theorem

A. L. Kanunnikov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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.

Key words: graded Goldie's rings, graded quotient rings.

UDC: 512.552.2

Received: 18.10.2010

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