Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2020, Cilt: 49 Sayı: 6, 2074 - 2083, 08.12.2020

Fatma Kaynarca Muhammed Ali Yıldırım

https://doi.org/10.15672/hujms.679606
Cited By: 1

Öz

Kaynakça

  • [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.

Reversibility of skew Hurwitz series rings

Yıl 2020, Cilt: 49 Sayı: 6, 2074 - 2083, 08.12.2020

Fatma Kaynarca Muhammed Ali Yıldırım

https://doi.org/10.15672/hujms.679606
Cited By: 1

Öz

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.

Anahtar Kelimeler

Skew Hurwitz series ring reversible ring α-rigid ring matrix ring

Kaynakça

  • [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.
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Fatma Kaynarca 0000-0002-5699-3369

Muhammed Ali Yıldırım 0000-0002-3940-2758

Yayımlanma Tarihi 8 Aralık 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 49 Sayı: 6

Kaynak Göster

APA Kaynarca, F., & Yıldırım, M. A. (2020). Reversibility of skew Hurwitz series rings. Hacettepe Journal of Mathematics and Statistics, 49(6), 2074-2083. https://doi.org/10.15672/hujms.679606
AMA Kaynarca F, Yıldırım MA. Reversibility of skew Hurwitz series rings. Hacettepe Journal of Mathematics and Statistics. Aralık 2020;49(6):2074-2083. doi:10.15672/hujms.679606
Chicago Kaynarca, Fatma, ve Muhammed Ali Yıldırım. “Reversibility of Skew Hurwitz Series Rings”. Hacettepe Journal of Mathematics and Statistics 49, sy. 6 (Aralık 2020): 2074-83. https://doi.org/10.15672/hujms.679606.
EndNote Kaynarca F, Yıldırım MA (01 Aralık 2020) Reversibility of skew Hurwitz series rings. Hacettepe Journal of Mathematics and Statistics 49 6 2074–2083.
IEEE F. Kaynarca ve M. A. Yıldırım, “Reversibility of skew Hurwitz series rings”, Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 6, ss. 2074–2083, 2020, doi: 10.15672/hujms.679606.
ISNAD Kaynarca, Fatma - Yıldırım, Muhammed Ali. “Reversibility of Skew Hurwitz Series Rings”. Hacettepe Journal of Mathematics and Statistics 49/6 (Aralık 2020), 2074-2083. https://doi.org/10.15672/hujms.679606.
JAMA Kaynarca F, Yıldırım MA. Reversibility of skew Hurwitz series rings. Hacettepe Journal of Mathematics and Statistics. 2020;49:2074–2083.
MLA Kaynarca, Fatma ve Muhammed Ali Yıldırım. “Reversibility of Skew Hurwitz Series Rings”. Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 6, 2020, ss. 2074-83, doi:10.15672/hujms.679606.
Vancouver Kaynarca F, Yıldırım MA. Reversibility of skew Hurwitz series rings. Hacettepe Journal of Mathematics and Statistics. 2020;49(6):2074-83.

Cited By

Skew Hurwitz Polinom Halkası Terslenebilir Olan Halkalar ve Genişlemeleri
Afyon Kocatepe University Journal of Sciences and Engineering
https://doi.org/10.35414/akufemubid.746509

https://dergipark.org.tr/en/pub/hujms