English

Subnearrings of $(\mathbb{Z}[x],+,\circ)$

Rings and Algebras 2020-11-30 v1

Abstract

We show that the nearring (Z[x],+,)(\mathbb{Z}[x],+,\circ) of integer polynomials, where the nearring multiplication is the composition of polynomials, has uncountably many subnearrings, and we give an explicit description of those nearrings that are generated by subsets of {1,x,x2,x3}\{1,x,x^2,x^3\}.

Keywords

Cite

@article{arxiv.1709.01345,
  title  = {Subnearrings of $(\mathbb{Z}[x],+,\circ)$},
  author = {Erhard Aichinger and Sebastian Kreinecker},
  journal= {arXiv preprint arXiv:1709.01345},
  year   = {2020}
}

Comments

22 pages