Homogeneous nilradicals over semigroup graded rings

Chan Hong , Kim Nam Kyun , Blake Madill , P. Nielsen , Michał Ziembowski

Abstract

In this paper we study the homogeneity of radicals defined by nilpotence or primality conditions, in rings graded by a semigroup S. When S is a unique product semigroup, we show that the right (and left) strongly prime and uniformly strongly prime radicals are homogeneous, and an even stronger result holds for the generalized nilradical. We further prove that rings graded by torsion-free, nilpotent groups have homogeneous upper nilradical. We conclude by showing that non-semiprime rings graded by a large class of semigroups must always contain nonzero homogeneous nilpotent ideals.
Author Chan Hong
Chan Hong,,
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, Kim Nam Kyun
Kim Nam Kyun,,
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, Blake Madill
Blake Madill,,
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, P. Nielsen
P. Nielsen,,
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, Michał Ziembowski (FMIS / DAC)
Michał Ziembowski,,
- Department of Algebra and Combinatorics
Journal seriesJournal of Pure and Applied Algebra, ISSN 0022-4049, (A 25 pkt)
Issue year2018
Vol222
No7
Pages1513-1528
Publication size in sheets0.75
Keywords in Polishpółgrupy, pierścienie zgradowane, radykały
Keywords in Englishsemigrups, graded rings, radicals
Abstract in PolishW tym artykule badamy homogeniczność radykałów definiowanych przez nilpotentność lub warunki związane z pierwszością, w pierścieniach zgradowanych przez półgrupę S. Gdy S jest u.p. półgrupą, pokazujemy, że prawe (i lewe) silnie pierwsze i jednolicie silnie pierwsze radykały są homogeniczne , a jeszcze silniejszy wynik dotyczy uogólnionego nilradyka.
DOIDOI:10.1016/j.jpaa.2017.07.009
URL https://www.sciencedirect.com/science/article/pii/S0022404917301597
Languageen angielski
Score (nominal)25
ScoreMinisterial score = 25.0, 12-07-2018, ArticleFromJournal
Ministerial score (2013-2016) = 25.0, 12-07-2018, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 0.652 (2) - 2016=0.608 (5)
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