Every simple compact semiring is finite
Rings and Algebras
2020-08-25 v2 General Topology
Abstract
A Hausdorff topological semiring is called simple if every non-zero continuous homomorphism into another Hausdorff topological semiring is injective. Classical work by Anzai and Kaplansky implies that any simple compact ring is finite. We generalize this result by proving that every simple compact semiring is finite, i.e., every infinite compact semiring admits a proper non-trivial quotient.
Cite
@article{arxiv.1509.01133,
title = {Every simple compact semiring is finite},
author = {Friedrich Martin Schneider and Jens Zumbrägel},
journal= {arXiv preprint arXiv:1509.01133},
year = {2020}
}
Comments
6 pages