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Two-sided essential nilpotence

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  • Esfandiar Eslami
  • Patrick Stewart

Abstract

An ideal I of a ring A is essentially nilpotent if I contains a nilpotent ideal N of A such that J ⋂ N ≠0 whenever J is a nonzero ideal of A contained in I . We show that each ring A has a unique largest essentially nilpotent ideal E N ( A ) . We study the properties of E N ( A ) and, in particular, we investigate how this ideal behaves with respect to related rings.

Suggested Citation

  • Esfandiar Eslami & Patrick Stewart, 1992. "Two-sided essential nilpotence," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 15, pages 1-4, January.
    • Handle: RePEc:hin:jijmms:829168
    DOI: 10.1155/S0161171292000449
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