KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2019 / Volume: 48 Issue: 6

On $J$-rigid rings

Soraya Karimi(Islamic Azad University)0000-0002-5690-4602
Shervin Sahebi(Islamic Azad University)0000-0003-0114-8798
Mohammad Habibi(Tafresh University)0000-0003-1317-1434
Sayfa
—
Yayın Tarihi
2019-12-08
🏛️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)

Moreover, we prove that every ring isomorphism preserves $J$-rigid structure, and several known results are extended.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:Let $R$ be a ring with an endomorphism $\sigma$.
📊
Temel Bulgular & Veri:We introduce the notion of $\sigma$-$J$-rigid rings as a generalization of $\sigma$-rigid rings, and investigate its properties.
💡
Sonuç & Katkı:Moreover, we prove that every ring isomorphism preserves $J$-rigid structure, and several known results are extended.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Rigid rings · Reduced rings · Jacobson radical

Abstract

Let $R$ be a ring with an endomorphism $\sigma$. We introduce the notion of $\sigma$-$J$-rigid rings as a generalization of $\sigma$-rigid rings, and investigate its properties. It is proved that a ring $R$ is $\sigma$-$J$-rigid if and only if $R[[x;\sigma]]$ is $\bar\sigma$-$J$-rigid, while the $\sigma$-$J$-rigid property is not Morita invariant. Moreover, we prove that every ring isomorphism preserves $J$-rigid structure, and several known results are extended.

🔖

Bu Makaleye Atıf Yap

Karimi, S., Sahebi, S., Habibi, M. (2019). On $J$-rigid rings. Hacettepe Journal of Mathematics and Statistics, Volume: 48 Issue: 6. https://doi.org/10.15672/HJMS.2018.646

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (13)

  1. S.A. Amitsur, Radicals of polynomial rings, Canad. J. Math. 8, 355–361, 1956.
  2. J. Chen, X. Yang, and Y. Zhou, On strongly clean matrix and triangular matrix rings, Comm. Algebra. 34, 3659–3674, 2006.
  3. W. Chen, Polynomial rings over weak Armendariz rings need not be weak Armendariz, Comm. Algebra. 42, 2528–2532, 2014.
  4. J. Dorroh, Concerning adjunctions to algebras, Bull. Amer. Math. Soc. 38 (2), 85–88, 1932.
  5. M. Habibi and A. Moussavi, Annihilator Properties of Skew Monoid Rings, Comm. Algebra, 42 (2), 842–852, 2014.
  6. M. Habibi, A. Moussavi and S. Mokhtari, On skew Armendariz of Laurent series type rings, Comm. Algebra, 40 (11), 3999–4018, 2012.
  7. C.Y. Hong, N.K. Kim and T.K. Kwak, Ore extensions of baer and pp-rings, J. Pure Appl. Algebra, 151 (3), 215–226, 2000.
  8. C.Y. Hong, N.K. Kim, and T.K. Kwak, On skew Armendariz rings, Comm. Algebra, 31 (1), 2511–2528, 2003.
  9. D. Jordan, Bijective extensions of injective ring endomorphisms, J. Lond. Math. Soc. 2 (3), 435–448, 1982.
  10. J. Krempa, Some examples of reduced rings, Algebra Colloq. 3, 289–300, 1996.
  11. J. Matczuk, A characterization of σ-rigid rings, Comm. Algebra, 32 (11), 4333–4336, 2004.
  12. K. Paykan and M. Habibi, Further results on Skew Monoid Rings of a certain free monoid, Cogent Math. Stat. 5 (1), 1–12, 2018.
  13. M. Sanaei, S. Sahebi, and H.H. Javadi, $\alpha$-skew $J$-Armendariz rings, J. Math. Ext. 12 (1), 63–72, 2018.