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arXiv · 1406.1932

Homomorphisms on infinite direct products of groups, rings and monoids

George M. Bergman
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Abstract

We study properties of a group, abelian group, ring, or monoid $B$ which (a) guarantee that every homomorphism from an infinite direct product $\prod_I A_i$ of objects of the same sort onto $B$ factors through the direct product of finitely many ultraproducts of the $A_i$ (possibly after composition with the natural map $B\to B/Z(B)$ or some variant), and/or (b) guarantee that when a map does so factor (and the index set has reasonable cardinality), the ultrafilters involved must be principal. A number of open questions, and topics for further investigation, are noted.

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George M. Bergman. 2014-06-07. Homomorphisms on infinite direct products of groups, rings and monoids. https://doi.org/10.2140/pjm.2015.274.451

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