Essentially nilpotent rings

descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 1971 English Publisher:Springer Science and Business Media LLCJournal:Israel Journal of Mathematics, volume 9, pages 180-185 (issn: 0021-2172, eissn: 1565-8511,

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Authors: Shock, R. C.;

doi: 10.1007/bf02771582

Essentially nilpotent rings

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Abstract

In this note we introduce a class of nil rings (called essentially nilpotent) which properly contains the class of nilpotent rings. A nil ring is said to be essentially nilpotent if it contains an essential right ideal which is nilpotent. Various properties of essentially nilpotent rings are investigated. A nil ring is essentially nilpotent if and only if it contains an essential right ideal which is leftT-nilpotent.

Related Organizations

Southern Illinois University Carbondale
United States

Keywords

Nil and nilpotent radicals, sets, ideals, associative rings

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