Abstract:
For an associative $\mathrm{gr}$-semiprime ring $R$ with identity graded by a group, the orthogonal graded completion $O^\mathrm{gr}(R)$ is constructed. A criterion for the orthogonal completeness of the maximal right graded quotient ring $Q^\mathrm{gr}(R)$ is proved. The ring $Q^\mathrm{gr}(R)$ need not be orthogonally complete, as opposed to the ungraded case.
Fulltext:
PDF file (337 kB)