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 Fundam. Prikl. Mat., 2016, Volume 21, Issue 2, Pages 187–191 (Mi fpm1725)

Goldie rings graded by a group with periodic quotient group modulo the center

A. L. Kanunnikov

Lomonosov Moscow State University

Abstract: In this paper, we study gr-prime and gr-semiprime Goldie rings graded by a group with periodic quotient group modulo the center. We enhance the theorem of Goodearl and Stafford (2000) about gr-prime rings graded by Abelian groups; we extend the Abelian group class to the class of groups with periodic quotient group modulo the center. We also decompose the orthogonal graded completion $O^{\mathrm{gr}}(R)$ of a gr-semiprime Goldie ring $R$ (graded by a group satisfying the same condition) into a direct sum of gr-prime Goldie rings $R_1,…, R_n$ and prove that the maximal graded quotient ring $Q^{\mathrm{gr}}(R)$ equals the direct sum of classical graded quotients rings of $R_1,…, R_n$.

 Funding Agency Grant Number Russian Foundation for Basic Research 14-01-00452_à

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English version:
Journal of Mathematical Sciences (New York), 2019, 237:2, 284–286

UDC: 512.552

Citation: A. L. Kanunnikov, “Goldie rings graded by a group with periodic quotient group modulo the center”, Fundam. Prikl. Mat., 21:2 (2016), 187–191; J. Math. Sci., 237:2 (2019), 284–286

Citation in format AMSBIB
\Bibitem{Kan16} \by A.~L.~Kanunnikov \paper Goldie rings graded by a group with periodic quotient group modulo the center \jour Fundam. Prikl. Mat. \yr 2016 \vol 21 \issue 2 \pages 187--191 \mathnet{http://mi.mathnet.ru/fpm1725} \transl \jour J. Math. Sci. \yr 2019 \vol 237 \issue 2 \pages 284--286 \crossref{https://doi.org/10.1007/s10958-019-4155-3}