Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 49 Sayı: 6, 1974 - 1987, 08.12.2020
https://doi.org/10.15672/hujms.571016

Öz

Kaynakça

  • [1] H.E. Bell, Near-rings in which each element is a power of itself, Bull. Austral. Math. Soc. 2, 363–368, 1970.
  • [2] H.E. Bell and Y. Li, Duo group rings, J. Pure Appl. Algebra, 209, 833–838, 2007.
  • [3] H.H. Brungs, Three questions on duo rings, Pacific J. Math. 58, 345–349, 1975.
  • [4] A.W. Chatters and C.R. Hajarnavis, Rings with Chain Conditions, Pitman Advanced Publishing Program, Boston, London, Melbourne, 1980.
  • [5] Y.W. Chung and Y. Lee, Structures concerning group of units, J. Korean Math. Soc. 54, 177–191, 2017.
  • [6] R.C. Courter, Finite dimensional right duo algebras are duo, Proc. Amer. Math. Soc. 84, 157–161, 1982.
  • [7] J.L. Dorroh, Concerning adjunctions to algebras, Bull. Amer. Math. Soc. 38, 85–88, 1932.
  • [8] E.H. Feller, Properties of primary noncommutative rings, Trans. Amer. Math. Soc. 89, 79–91, 1958.
  • [9] K.R. Goodearl, Von Neumann Regular Rings, Pitman, London, 1979.
  • [10] K.R. Goodearl and R.B. Warfield, Jr., An Introduction to Noncommutative Noetherian Rings, London Mathematical Society Student Texts 16, Cambridge University Press, Cambridge, 1989.
  • [11] I.N. Herstein and L.W. Small, Nil rings satisfying certain chain conditions, Canad. J. Math. 16, 771–776, 1964.
  • [12] I.N. Herstein and L.W. Small, Addendum to “Nil rings satisfying certain chain conditions", Canad. J. Math. 18, 300–302, 1966.
  • [13] C. Huh, H.K. Kim and Y. Lee, p.p. rings and generalized p.p. rings, J. Pure Appl. Algebra, 16, 37–52, 2002.
  • [14] C. Huh, Y. Lee and A. Smoktunowicz, Armendariz rings and semicommutative ring, Comm. Algebra, 30, 751–761, 2002.
  • [15] S.U. Hwang, Y.C. Jeon and Y. Lee, Structure and topological conditions of NI rings, J. Algebra , 302, 186–199, 2006.
  • [16] H.K. Kim, N.K. Kim and Y. Lee, Weakly duo rings with nil Jacobson radical, J. Korean Math. Soc. 42, 455-468, 2005.
  • [17] C. Lanski, Nil subrings of Goldie rings are nilpotent, Canad. J. Math. 21, 904–907, 1969.
  • [18] B. Li, On potent rings, Commun. Korean Math. Soc. 23, 161–167, 2008.
  • [19] G. Marks, On 2-primal Ore extensions, Comm. Algebra, 29, 2113–2123, 2001.
  • [20] G. Marks, Duo rings and Ore extensions, J. Algebra, 280, 463–471, 2004.
  • [21] J.C. McConnell, J.C. Robson, Noncommutative Noetherian Rings, John Wiley & Sons Ltd., Chichester, New York, Brisbane, Toronto, Singapore, 1987.
  • [22] W.K. Nicholson, I-rings, Trans. Amer. Math. Soc. 207, 361–373, 1975.
  • [23] W.K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc. 229 , 269–278, 1977.
  • [24] C. Polcino Milies and S.K. Sehgal, An Introduction to Group Rings, Kluwer Academic Publishers, Dordrecht, 2002.
  • [25] G. Thierrin, On duo rings, Canad. Math. Bull. 3, 167–172, 1960.
  • [26] X. Yao, Weakly right duo rings, Pure Appl. Math. Sci. 21, 19–24, 1985.

One-sided duo property on nilpotents

Yıl 2020, Cilt: 49 Sayı: 6, 1974 - 1987, 08.12.2020
https://doi.org/10.15672/hujms.571016

Öz

We study the structure of nilpotents in relation with a ring property that is near to one-sided  duo rings. Such a property is said to be one-sided nilpotent-duo. We prove the following for a one-sided nilpotent-duo  ring $R$: (i) The set of nilpotents in $R$ forms a subring; (ii) Köthe's conjecture holds for $R$; (iii) the subring generated by the identity and the set of nilpotents in $R$ is a  one-sided  duo ring; (iv) if the polynomial ring $R[x]$ over $R$ is  one-sided  nilpotent-duo then the set of nilpotents in $R$ forms a commutative ring, and $R[x]$ is an NI ring.  Several connections between  one-sided  nilpotent-duo and  one-sided duo are given. The structure of one-sided nilpotent-duo rings is also studied in various situations in ring theory. Especially we investigate several kinds of conditions under which  one-sided  nilpotent-duo rings are NI.

Kaynakça

  • [1] H.E. Bell, Near-rings in which each element is a power of itself, Bull. Austral. Math. Soc. 2, 363–368, 1970.
  • [2] H.E. Bell and Y. Li, Duo group rings, J. Pure Appl. Algebra, 209, 833–838, 2007.
  • [3] H.H. Brungs, Three questions on duo rings, Pacific J. Math. 58, 345–349, 1975.
  • [4] A.W. Chatters and C.R. Hajarnavis, Rings with Chain Conditions, Pitman Advanced Publishing Program, Boston, London, Melbourne, 1980.
  • [5] Y.W. Chung and Y. Lee, Structures concerning group of units, J. Korean Math. Soc. 54, 177–191, 2017.
  • [6] R.C. Courter, Finite dimensional right duo algebras are duo, Proc. Amer. Math. Soc. 84, 157–161, 1982.
  • [7] J.L. Dorroh, Concerning adjunctions to algebras, Bull. Amer. Math. Soc. 38, 85–88, 1932.
  • [8] E.H. Feller, Properties of primary noncommutative rings, Trans. Amer. Math. Soc. 89, 79–91, 1958.
  • [9] K.R. Goodearl, Von Neumann Regular Rings, Pitman, London, 1979.
  • [10] K.R. Goodearl and R.B. Warfield, Jr., An Introduction to Noncommutative Noetherian Rings, London Mathematical Society Student Texts 16, Cambridge University Press, Cambridge, 1989.
  • [11] I.N. Herstein and L.W. Small, Nil rings satisfying certain chain conditions, Canad. J. Math. 16, 771–776, 1964.
  • [12] I.N. Herstein and L.W. Small, Addendum to “Nil rings satisfying certain chain conditions", Canad. J. Math. 18, 300–302, 1966.
  • [13] C. Huh, H.K. Kim and Y. Lee, p.p. rings and generalized p.p. rings, J. Pure Appl. Algebra, 16, 37–52, 2002.
  • [14] C. Huh, Y. Lee and A. Smoktunowicz, Armendariz rings and semicommutative ring, Comm. Algebra, 30, 751–761, 2002.
  • [15] S.U. Hwang, Y.C. Jeon and Y. Lee, Structure and topological conditions of NI rings, J. Algebra , 302, 186–199, 2006.
  • [16] H.K. Kim, N.K. Kim and Y. Lee, Weakly duo rings with nil Jacobson radical, J. Korean Math. Soc. 42, 455-468, 2005.
  • [17] C. Lanski, Nil subrings of Goldie rings are nilpotent, Canad. J. Math. 21, 904–907, 1969.
  • [18] B. Li, On potent rings, Commun. Korean Math. Soc. 23, 161–167, 2008.
  • [19] G. Marks, On 2-primal Ore extensions, Comm. Algebra, 29, 2113–2123, 2001.
  • [20] G. Marks, Duo rings and Ore extensions, J. Algebra, 280, 463–471, 2004.
  • [21] J.C. McConnell, J.C. Robson, Noncommutative Noetherian Rings, John Wiley & Sons Ltd., Chichester, New York, Brisbane, Toronto, Singapore, 1987.
  • [22] W.K. Nicholson, I-rings, Trans. Amer. Math. Soc. 207, 361–373, 1975.
  • [23] W.K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc. 229 , 269–278, 1977.
  • [24] C. Polcino Milies and S.K. Sehgal, An Introduction to Group Rings, Kluwer Academic Publishers, Dordrecht, 2002.
  • [25] G. Thierrin, On duo rings, Canad. Math. Bull. 3, 167–172, 1960.
  • [26] X. Yao, Weakly right duo rings, Pure Appl. Math. Sci. 21, 19–24, 1985.
Toplam 26 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Chan Yong Hong Bu kişi benim 0000-0003-1984-2841

Hong Kee Kim Bu kişi benim 0000-0002-4367-1715

Nam Kyun Kim 0000-0002-4419-9045

Tai Keun Kwak 0000-0001-6316-8650

Yang Lee Bu kişi benim 0000-0002-7572-5191

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

Kaynak Göster

APA Hong, C. Y., Kim, H. K., Kim, N. K., Kwak, T. K., vd. (2020). One-sided duo property on nilpotents. Hacettepe Journal of Mathematics and Statistics, 49(6), 1974-1987. https://doi.org/10.15672/hujms.571016
AMA Hong CY, Kim HK, Kim NK, Kwak TK, Lee Y. One-sided duo property on nilpotents. Hacettepe Journal of Mathematics and Statistics. Aralık 2020;49(6):1974-1987. doi:10.15672/hujms.571016
Chicago Hong, Chan Yong, Hong Kee Kim, Nam Kyun Kim, Tai Keun Kwak, ve Yang Lee. “One-Sided Duo Property on Nilpotents”. Hacettepe Journal of Mathematics and Statistics 49, sy. 6 (Aralık 2020): 1974-87. https://doi.org/10.15672/hujms.571016.
EndNote Hong CY, Kim HK, Kim NK, Kwak TK, Lee Y (01 Aralık 2020) One-sided duo property on nilpotents. Hacettepe Journal of Mathematics and Statistics 49 6 1974–1987.
IEEE C. Y. Hong, H. K. Kim, N. K. Kim, T. K. Kwak, ve Y. Lee, “One-sided duo property on nilpotents”, Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 6, ss. 1974–1987, 2020, doi: 10.15672/hujms.571016.
ISNAD Hong, Chan Yong vd. “One-Sided Duo Property on Nilpotents”. Hacettepe Journal of Mathematics and Statistics 49/6 (Aralık 2020), 1974-1987. https://doi.org/10.15672/hujms.571016.
JAMA Hong CY, Kim HK, Kim NK, Kwak TK, Lee Y. One-sided duo property on nilpotents. Hacettepe Journal of Mathematics and Statistics. 2020;49:1974–1987.
MLA Hong, Chan Yong vd. “One-Sided Duo Property on Nilpotents”. Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 6, 2020, ss. 1974-87, doi:10.15672/hujms.571016.
Vancouver Hong CY, Kim HK, Kim NK, Kwak TK, Lee Y. One-sided duo property on nilpotents. Hacettepe Journal of Mathematics and Statistics. 2020;49(6):1974-87.

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