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Bull. Korean Math. Soc. 2019; 56(1): 23-29

Online first article January 14, 2019      Printed January 31, 2019

https://doi.org/10.4134/BKMS.b180030

Copyright © The Korean Mathematical Society.

On fully filial torsion rings

Ryszard Romuald Andruszkiewicz, Karol Pryszczepko

University of Bia{\l}ystok; University of Bia{\l}ystok

Abstract

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Rings in which all accessible subrings are ideals are called filial. A ring $R$ is called fully filial if all its subrings are filial (that is rings in which the relation of being an ideal is transitive). The present paper is devoted to the study of fully filial torsion rings. We prove a classification theorem for semiprime fully filial torsion rings.

Keywords: ideal, $H$-ring, filial ring, J-ring

MSC numbers: 16D25, 13C05

Supported by: This publication has received financial support
from the Polish Ministry of Science and Higher Education under subsidy for maintaining the research potential of the Faculty of Mathematics, University of Białystok.

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