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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 46 Issue: 2

Monoids over which products of indecomposable acts are indecomposable

Mojtaba Sedaghatjoo
Ahmad Khaksari
Pages
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Publication Date
2017-04-01
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Ultimately, we prove that the one element right $S$ -act $\Theta_S$ is product flat if and only if $S$ contains a left zero.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we prove that for a monoid $S$, products of indecomposable right $S$ -acts are indecomposable if and only if $S$ contains a right zero.
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Key Findings & Data:Besides, we prove that subacts of indecomposable right $S$ -acts are indecomposable if and only if $S$ is left reversible.
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Conclusion & Impact:Ultimately, we prove that the one element right $S$ -act $\Theta_S$ is product flat if and only if $S$ contains a left zero.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Indecomposable act · left reversible monoid · Baer criterion

Abstract

In this paper we prove that for a monoid $S$, products of indecomposable right $S$ -acts are indecomposable if and only if $S$ contains a right zero. Besides, we prove that subacts of indecomposable right $S$ -acts are indecomposable if and only if $S$ is left reversible. Ultimately, we prove that the one element right $S$ -act $\Theta_S$ is product flat if and only if $S$ contains a left zero.

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Cite This Article

Sedaghatjoo, M., Khaksari, A. (2017). Monoids over which products of indecomposable acts are indecomposable. Hacettepe Journal of Mathematics and Statistics, Volume: 46 Issue: 2. https://ajindex.com/articles/1403049

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References (9)

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