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 Fundam. Prikl. Mat., 2012, Volume 17, Issue 4, Pages 83–93 (Mi fpm1422)

M. Vuković, E. Ilić-Georgijević

University of Sarajevo, Bosnia and Herzegovina

Abstract: The notions of a paragraded ring and a homogeneous ideal, which are at the same time a generalization of the classical graduation, as defined by Bourbaki, and an extension of the earlier work done by M. Krasner, were introduced by M. Krasner and M. Vuković. After recalling the notion of paragraded rings, we list out and prove several facts about them. One of the most important properties is that the homogeneous part of the direct product and the direct sum of paragraded rings are the direct product and the direct sum of the corresponding homogeneous parts, respectively. Next we give the notion of a homogeneous ideal of a paragraded ring and prove that the factor ring obtained from a paragraded ring and its homogeneous ideal is also a paragraded ring. After that, we deal with basic facts about homogeneous ideals.

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English version:
Journal of Mathematical Sciences (New York), 2013, 191:5, 654–660

UDC: 512.552

Citation: M. Vuković, E. Ilić-Georgijević, “Paragraded rings and their ideals”, Fundam. Prikl. Mat., 17:4 (2012), 83–93; J. Math. Sci., 191:5 (2013), 654–660

Citation in format AMSBIB
\Bibitem{VukIli12} \by M.~Vukovi{\'c}, E.~Ili{\'c}-Georgijevi{\'c} \paper Paragraded rings and their ideals \jour Fundam. Prikl. Mat. \yr 2012 \vol 17 \issue 4 \pages 83--93 \mathnet{http://mi.mathnet.ru/fpm1422} \transl \jour J. Math. Sci. \yr 2013 \vol 191 \issue 5 \pages 654--660 \crossref{https://doi.org/10.1007/s10958-013-1349-y} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84884988318} 

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This publication is cited in the following articles:
1. E. Ilić-Georgijević, M. Vuković, “The Wedderburn–Artin theorem for paragraded rings”, J. Math. Sci., 221:3 (2017), 391–400
2. Emil Ilić-Georgijević, Mirjana Vuković, “Primary decomposition of general graded structures”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2015, no. 1, 87–96
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