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Journals / Hacettepe Journal of Mathematics and Statistics / 2017 / Cilt: 46 - Sayı: 2

Monoids over which products of indecomposable acts are indecomposable

Ahmad KHAKSARİ
Mojtaba SEDAGHATJOO
Pages
229–237
Publication Date
2022-10-18
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 rightzero.
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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 rightzero. 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

KHAKSARİ, A., SEDAGHATJOO, M. (2022). Monoids over which products of indecomposable acts are indecomposable. Hacettepe Journal of Mathematics and Statistics, Cilt: 46 - Sayı: 2, 229–237. https://ajindex.com/articles/529961

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References (9)

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