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arXiv · 2111.13922

The Jordan-H\"older Theorem for Monoids with Group Action

Alfilgen Sebandal·Jocelyn P. Vilela
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Abstract

In this article, we prove an isomorphism theorem for the case of refinement $\Gamma$-monoids. Based on this we show a version of the well-known Jordan-H\"older theorem in this framework. The main theorem of this article states that - as in the case of modules - a monoid $T$ has a $\Gamma$-composition series if and only if it is both $\Gamma$-Noetherian and $\Gamma$-Artinian. As in module theory, these two concepts can be defined via ascending and descending chains respectively.

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Alfilgen Sebandal, Jocelyn P. Vilela. 2021-11-27. The Jordan-H\"older Theorem for Monoids with Group Action. https://doi.org/10.1142/s0219498823500883

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