KaydedilenlerDerginizi ekleyin

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

Monoids over which products of indecomposable acts are indecomposable

Mojtaba Sedaghatjoo
Ahmad Khaksari
Sayfa
—
Yayın Tarihi
2017-04-01
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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 Maddede Bu Makale

🎯
Amaç & Hipotez: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.
📊
Temel Bulgular & Veri:Besides, we prove that subacts of indecomposable right $S$ -acts are indecomposable if and only if $S$ is left reversible.
💡
Sonuç & Katkı:Ultimately, we prove that the one element right $S$ -act $\Theta_S$ is product flat if and only if $S$ contains a left zero.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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.

🔖

Bu Makaleye Atıf Yap

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

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (9)

  1. Adamek, J., Herrlich, H. and Strecker, G. Abstract and Concrete Categories The Joy of Cats (John Wiley and Sons, New York, 1990).
  2. Bulman-Fleming, S. Products of projective S-systems, Comm. Algebra 19 (3), 951964, 1991.
  3. Bulman-Fleming, S. and Laan, V. Tensor products and preservation of limits, for acts over monoids, Semigroup Forum 63, 161179, 2001.
  4. Bulman-Fleming, S and McDowell, K. Coherent monoids, in: Latices, Semigroups and Universal Algebra, ed. J. Almeida et al. (Plenum Press, New York, 1990).
  5. Gould, V. Coherent monoids, J. Austral. Math. Soc. 53(Series A), 166182, 1992.
  6. Kilp, M., Knauer, U. and Mikhalev, A. Monoids, Acts and Categories, (W. de gruyter, Berlin, 2000).
  7. Nico, W.R. A classication of indecomposable S-sets, J. Algebra 54(1), 260272, 1978.
  8. Renshaw, J. Monoids for which condition (P)acts are projective, Semigroup Forum 61(1), 4656, 1998.
  9. Sedaghatjoo, M., Khosravi, R. and Ershad, M. Principally weakly and weakly coherent monoids, Comm. Algebra 37(12), 42814295, 2009.