GRADED RINGS WITH FINITENESS CONDITIONS

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.
Throughout the paper, [member of] is a group with neutral element e, R is an associative ring graded by G, i.e., [Please download the PDF to view the mathematical expression], [...]