KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2020 / Volume: 49 Issue: 6

Reversibility of skew Hurwitz series rings

Fatma Kaynarca(AFYON KOCATEPE UNIVERSITY)0000-0002-5699-3369
Muhammed Ali Yıldırım(AFYON KOCATEPE UNIVERSITY)0000-0002-3940-2758
Sayfa
—
Yayın Tarihi
2020-12-08
🏛️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)

We examine some characterizations and extensions of $SH$-reversible rings in relation with several ring theoretic properties which have roles in ring theory.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:We study the reversibility of skew Hurwitz series at zero as a generalization of an $\alpha$-rigid ring, introducing the concept of skew Hurwitz reversibility.
📊
Temel Bulgular & Veri:A ring $R$ is called skew Hurwitz reversible ($SH$-reversible, for short), if the skew Hurwitz series ring $(HR,\alpha)$ is reversible i.e. whenever skew Hurwitz series $f, g\in (HR,\alpha)$ satisfy $fg=0$, then $gf=0$.
💡
Sonuç & Katkı:We examine some characterizations and extensions of $SH$-reversible rings in relation with several ring theoretic properties which have roles in ring theory.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Skew Hurwitz series ring · reversible ring · α-rigid ring

Abstract

We study the reversibility of skew Hurwitz series at zero as a generalization of an $\alpha$-rigid ring, introducing the concept of skew Hurwitz reversibility. A ring $R$ is called skew Hurwitz reversible ($SH$-reversible, for short), if the skew Hurwitz series ring $(HR,\alpha)$ is reversible i.e. whenever skew Hurwitz series $f, g\in (HR,\alpha)$ satisfy $fg=0$, then $gf=0$. We examine some characterizations and extensions of $SH$-reversible rings in relation with several ring theoretic properties which have roles in ring theory.

🔖

Bu Makaleye Atıf Yap

Kaynarca, F., Yıldırım, M. A. (2020). Reversibility of skew Hurwitz series rings. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 6. https://doi.org/10.15672/hujms.679606

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (24)

  1. M. Ahmadi, A. Moussavi and V. Nourozi, On skew Hurwitz serieswise Armendariz rings, Asian-Eur. J. Math. 7 (3), 1450036, 2014.
  2. D.D. Anderson and V. Camillo, Semigroups and rings whose zero products commute, Comm. Algebra, 27 (6), 2847–2852, 1999.
  3. M. Başer, C.Y. Hong and T.K. Kwak, On Extended Reversible Rings, Algebra Colloq. 16 (1), 37–48, 2009.
  4. A. Benhissi and F. Koja, Basic propoerties of Hurwitz series rings, Ric. Mat. 61, 255–273, 2012.
  5. P.M. Cohn, Reversible rings, Bull. Lond. Math. Soc. 31, 641–648, 1999.
  6. E. Hashemi and A. Moussavi, Polynomial extensions of quasi-Baer rings, Acta Math. Hungar. 3, 207–224, 2005.
  7. A.M Hassanein, Clean rings of skew hurwitz series, Matematiche, 62 (1), 47–54, 2007.
  8. A.M. Hassanein, On uniquely clean skew Hurwitz series, Southeast Asian Bull. Math. 35, 5-10, 2012.
  9. C.Y. Hong, N.K. Kim and T.K. Kwak, Ore extensions of Baer and p.p.-rings, J. Pure Appl. Algebra, 151, 215–226, 2000.
  10. C.Y. Hong, N.K. Kim and T.K. Kwak, On skew Armendariz rings, Comm. Algebra, 31, 103–122, 2003.
  11. C.Y. Hong, T.K. Kwak and S.T. Rizvi, Extensions of generalized Armendariz rings, Algebra Colloq. 13, 253–266, 2006.
  12. H.L. Jin, F. Kaynarca, T.K. Kwak and Y. Lee, On commutativity of skew polynomials at zero, Bull. Korean Math. Soc. 54, 51–69, 2017.
  13. W.F. Keigher, Adjunctions and comonads in differential algebra, Pacific J. Math. 59, 99–112, 1975.
  14. W.F. Keigher, On the ring of Hurwitz Series, Comm. Algebra, 25 (6), 1845–1859, 1997.
  15. W.F. Keigher and F.L. Pritchard, Hurwitz series as formal functions, J. Pure Appl. Algebra, 146, 291-304, 2000.
  16. N.K. Kim and Y. Lee, Extensions of reversible rings, J. Pure Appl. Algebra, 185, 207–223, 2003.
  17. J. Krempa, Some examples of reduced rings, Algebra Colloq. 3 (4), 289–300, 1996.
  18. J. Krempa and D. Niewieczerzal, Rings in which annihilators are ideals and their application to semigroup rings, Bull. Acad. Polon. Sci. Ser. Sci., Math. Astronom. Phys, 25, 851-856, 1977.
  19. J. Lambek, On the representation of modules by sheaves of factor modules, Canad. Math. Bull. 14 (3), 359-368, 1971.
  20. K. Paykan, A study on skew Hurwitz series ring, Ric. Mat. 66 (2), 383–393, 2016.
  21. K. Paykan, Principally quasi-Baer skew Hurwitz series rings, Boll. Unione Mat. Ital. 10 (4), 607–616, 2017.
  22. M.B. Rege and S. Chhawchharia, Armendariz rings, Proc. Japan Acad. Ser. A Math. Sci. 73, 14–17, 1997.
  23. S. Veldsman, Matrix and polynomial reversibility of rings, Comm. Algebra, 43, 1571– 1582, 2015.
  24. G. Yang and Z.K. Liu, On strongly reversible rings, Taiwanese J. Math. 12 (1), 129– 136, 2008.