Every simple compact semiring is finite

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• 作者：Friedrich Martin Schneider^a ; ^{martin.schneider@tu-dresden.de" class="auth_mail" title="E-mail the corresponding author} ; Jens Zumbrä ; gel^b ; ^{jens.zumbragel@epfl.ch" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 16Y60 ; secondary ; 54H13
• 刊名：Topology and its Applications
• 出版年：2016
• 出版时间：15 June 2016
• 年：2016
• 卷：206
• 期：Complete
• 页码：305-310
• 全文大小：256 K

文摘

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.