Every simple compact semiring is finite

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. (C) 2016 Elsevier B.V. All rights reserved.


Published in:
Topology And Its Applications, 206, 305-310
Year:
2016
Publisher:
Amsterdam, Elsevier Science Bv
ISSN:
0166-8641
Keywords:
Laboratories:




 Record created 2016-07-19, last modified 2018-03-17


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