Zero-divisor graphs of nilpotent-free semigroups
Abstract
We find strong relationships between the zero-divisor graphs of apparently disparate kinds of nilpotent-free semigroups by introducing the notion of an \emph{Armendariz map} between such semigroups, which preserves many graph-theoretic invariants. We use it to give relationships between the zero-divisor graph of a ring, a polynomial ring, and the annihilating-ideal graph. Then we give relationships between the zero-divisor graphs of certain topological spaces (so-called pearled spaces), prime spectra, maximal spectra, tensor-product semigroups, and the semigroup of ideals under addition, obtaining surprisingly strong structure theorems relating ring-theoretic and topological properties to graph-theoretic invariants of the corresponding graphs.
Keywords
Cite
@article{arxiv.1112.0185,
title = {Zero-divisor graphs of nilpotent-free semigroups},
author = {Neil Epstein and Peyman Nasehpour},
journal= {arXiv preprint arXiv:1112.0185},
year = {2015}
}
Comments
Expanded first paragraph in section 6. To appear in J. Algebraic Combin. 22 pages