On subhereditary radicals and reduced rings

K. I. Beidar; W. F. Ke; E. R. Puczyłowski

doi:10.1017/s030821050000161x

On subhereditary radicals and reduced rings

K. I. Beidar, W. F. Ke, E. R. Puczyłowski

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We answer some open problems on subhereditary radicals of associative rings. In particular, we show that the Brown-McCoy radical is not subhereditary and that every left or right subhereditary and left or right stable radical satisfies all these properties. The latter of these results concerns, in fact, the question whether some classes of reduced rings are closed under one-sided essential extensions. We characterize several such classes.

Original language	English
Pages (from-to)	255-266
Number of pages	12
Journal	Royal Society of Edinburgh - Proceedings A
Volume	132
Issue number	2
DOIs	https://doi.org/10.1017/s030821050000161x
Publication status	Published - 2002

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1017/s030821050000161x

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title = "On subhereditary radicals and reduced rings",

abstract = "We answer some open problems on subhereditary radicals of associative rings. In particular, we show that the Brown-McCoy radical is not subhereditary and that every left or right subhereditary and left or right stable radical satisfies all these properties. The latter of these results concerns, in fact, the question whether some classes of reduced rings are closed under one-sided essential extensions. We characterize several such classes.",

author = "Beidar, {K. I.} and Ke, {W. F.} and Puczy{\l}owski, {E. R.}",

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language = "English",

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AU - Beidar, K. I.

AU - Ke, W. F.

AU - Puczyłowski, E. R.

N1 - Funding Information: E.R..Pwasuppsorted by KBN grant no. 2-PO3A-039-14 and National Cheng-Kung Unieviry,tTsanan,iTaiawn.

PY - 2002

Y1 - 2002

N2 - We answer some open problems on subhereditary radicals of associative rings. In particular, we show that the Brown-McCoy radical is not subhereditary and that every left or right subhereditary and left or right stable radical satisfies all these properties. The latter of these results concerns, in fact, the question whether some classes of reduced rings are closed under one-sided essential extensions. We characterize several such classes.

AB - We answer some open problems on subhereditary radicals of associative rings. In particular, we show that the Brown-McCoy radical is not subhereditary and that every left or right subhereditary and left or right stable radical satisfies all these properties. The latter of these results concerns, in fact, the question whether some classes of reduced rings are closed under one-sided essential extensions. We characterize several such classes.

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JO - Royal Society of Edinburgh - Proceedings A

JF - Royal Society of Edinburgh - Proceedings A

IS - 2

ER -

On subhereditary radicals and reduced rings

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