English

Nil-Essential Ideals

Rings and Algebras 2024-01-17 v1

Abstract

The class of nil-essential ideals is a generalisation of the class of essential ideals. Every nil-essential ideal of a reduced ring is essential. Therefore the intersection of all nil-essential ideals over a reduced ring RR is the socle of RR. In this note, we apply this generalisation to give a new criteria of semisimplicity in terms of nil-essentiality of ideals.

Keywords

Cite

@article{arxiv.2401.08535,
  title  = {Nil-Essential Ideals},
  author = {Raplang Nongsiej and Ardeline Mary Buhphang},
  journal= {arXiv preprint arXiv:2401.08535},
  year   = {2024}
}

Comments

5 pages, this work needs to be completed

R2 v1 2026-06-28T14:18:17.181Z