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Tbilisi Mathematical Journal

Editor-in-Chief: Inassaridze, Hvedri

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On radical classes of hemirings

Hvedri Inassaridze / Le Hoang Mai / Nguyen Xuan Tuyen
Published Online: 2014-11-12 | DOI: https://doi.org/10.2478/tmj-2014-0007


Based on the concept of accessible subhemirings and inspired by the work on the general Kurosh-Amitsur radical theory for rings, this paper studies the lower radical classes and the hereditary radical classes of hemirings. We characterize radical classes of hemirings, and con- struct a lower radical class from a homomorphically closed class. We provide a necessary and sufficient condition under which an upper radical class of hemirings becomes hereditary and prove that an upper radical class of a regular class of semirings is hereditary. Besides, we show that the Brown-McCoy radical class and a Jacobson-type radical class are hereditary.

MSC: 16Y60; 8A30; 06A99; 06F99; 18G05; 18G99

Keywords: accessible subhemiring; radical class of hemirings; lower radical class; upper radical class; hereditary radical class of hemiring


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About the article

Received: 2013-07-13

Accepted: 2014-10-08

Published Online: 2014-11-12

Citation Information: Tbilisi Mathematical Journal, Volume 7, Issue 1, ISSN (Online) 1512-0139, DOI: https://doi.org/10.2478/tmj-2014-0007.

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© 2014 MHvedri Inassaridze, Le Hoang Mai, Nguyen Xuan Tuyen. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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