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Yıl 2020, Cilt: 49 Sayı: 4, 1397 - 1404, 06.08.2020

M. Tamer Koşan Truong Cong Quynh Tülay Yıldırım Jan žemlička

https://doi.org/10.15672/hujms.542574
Cited By: 3

Öz

Kaynakça

  • [1] D.D. Anderson, D. Bennis, B. Fahid and A. Shaiea, On n-trivial extensions of rings, Rocky Mountain. J. Math. 47, 2439–2511, 2017.
  • [2] A. Badawi, On abelian π-regular rings, Comm. Algebra, 25 (4), 1009–1021, 1997.
  • [3] G.F. Birkenmeier, H.E. Heatherly, and E.K. Lee, Completely prime ideals and associated radicals, Proc. Biennial Ohio State-Denison Conference 1992, edited by S. K. Jain and S. T. Rizvi, World Scientific, Singapore-New Jersey-London-Hong Kong, 102–129, 1993.
  • [4] G. Calugareanu, UU rings, Carpathian J. Math. 31 (2), 157–163, 2015.
  • [5] J. Cui and X. Yin, Rings with 2-UJ property, Comm. Algebra, 48 (4), 1382–1391, 2020.
  • [6] P. Danchev, Rings with Jacobson units, Toyama Math. J. 38, 61–74, 2016.
  • [7] P. Danchev and T.Y. Lam, Rings with unipotent units, Publ. Math. Debrecen, 88 (3-4), 449–466, 2016.
  • [8] P. Danchev and J. Matczuk, n-torsion clean rings, in: Rings, modules and codes, Contemp. Math. 727, Amer. Math. Soc. Providence, RI, 71–82, 2019.
  • [9] J. Han and W.K. Nicholson, Extension of clean rings, Comm. Algebra, 29 (6), 2589– 2595, 2001.
  • [10] I. Kaplansky, Rings with a polynomial identity, Bull. Amer. Math. Soc. 54 (6), 575– 580, 1948.
  • [11] M.T. Koşan, The p.p. property of trivial extensions, J. Algebra Appl. 14 (8), 1550124, 5 pp., 2015.
  • [12] M.T. Koşan, A. Leroy and J. Matczuk, On UJ-rings, Comm. Algebra, 46 (5), 2297– 2303, 2018.
  • [13] T.Y. Lam, A First Course in Noncommutative Rings (second Ed.), Springer Verlag, New York, 2001.
  • [14] J. Levitzki, On the structure of algebraic algebras and related rings, Trans. Amer. Math. Soc. 74, 384–409, 1953.
  • [15] M. Marianne, Rings of quotients of generalized matrix rings, Comm. Algebra, 15 (10), 1991–2015, 1987.
  • [16] W.K. Nicholson, Semiregular modules and rings, Canad. J. Math. 28 (5), 1105–1120, 1976.
  • [17] W.K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc. 229, 269-278, 1977.
  • [18] W.K. Nicholson, Strongly clean rings and Fittings lemma, Comm. Algebra, 27, 3583– 3592, 1999.
  • [19] S. Sahinkaya and T. Yildirim, UJ-endomorphism rings, The Mathematica Journal, 60 (83), 186–198, 2018.

Rings such that, for each unit u, u − u n belongs to the Jacobson radical

Yıl 2020, Cilt: 49 Sayı: 4, 1397 - 1404, 06.08.2020

M. Tamer Koşan Truong Cong Quynh Tülay Yıldırım Jan žemlička

https://doi.org/10.15672/hujms.542574
Cited By: 3

Öz

A ring R is said to be n-UJ if u − u n ∈ J(R) for each unit u of R, where n > 1 is a fixed integer. In this paper, the structure of n-UJ rings is studied under various conditions. Moreover, the n-UJ property is studied under some algebraic constructions. Mathematics Subject Classification (2010). 16N20, 16D60, 16U60, 16W10

Anahtar Kelimeler

UU-ring UJ-ring unit Jacobson radical clean ring (semi)regular ring reduced ring

Kaynakça

  • [1] D.D. Anderson, D. Bennis, B. Fahid and A. Shaiea, On n-trivial extensions of rings, Rocky Mountain. J. Math. 47, 2439–2511, 2017.
  • [2] A. Badawi, On abelian π-regular rings, Comm. Algebra, 25 (4), 1009–1021, 1997.
  • [3] G.F. Birkenmeier, H.E. Heatherly, and E.K. Lee, Completely prime ideals and associated radicals, Proc. Biennial Ohio State-Denison Conference 1992, edited by S. K. Jain and S. T. Rizvi, World Scientific, Singapore-New Jersey-London-Hong Kong, 102–129, 1993.
  • [4] G. Calugareanu, UU rings, Carpathian J. Math. 31 (2), 157–163, 2015.
  • [5] J. Cui and X. Yin, Rings with 2-UJ property, Comm. Algebra, 48 (4), 1382–1391, 2020.
  • [6] P. Danchev, Rings with Jacobson units, Toyama Math. J. 38, 61–74, 2016.
  • [7] P. Danchev and T.Y. Lam, Rings with unipotent units, Publ. Math. Debrecen, 88 (3-4), 449–466, 2016.
  • [8] P. Danchev and J. Matczuk, n-torsion clean rings, in: Rings, modules and codes, Contemp. Math. 727, Amer. Math. Soc. Providence, RI, 71–82, 2019.
  • [9] J. Han and W.K. Nicholson, Extension of clean rings, Comm. Algebra, 29 (6), 2589– 2595, 2001.
  • [10] I. Kaplansky, Rings with a polynomial identity, Bull. Amer. Math. Soc. 54 (6), 575– 580, 1948.
  • [11] M.T. Koşan, The p.p. property of trivial extensions, J. Algebra Appl. 14 (8), 1550124, 5 pp., 2015.
  • [12] M.T. Koşan, A. Leroy and J. Matczuk, On UJ-rings, Comm. Algebra, 46 (5), 2297– 2303, 2018.
  • [13] T.Y. Lam, A First Course in Noncommutative Rings (second Ed.), Springer Verlag, New York, 2001.
  • [14] J. Levitzki, On the structure of algebraic algebras and related rings, Trans. Amer. Math. Soc. 74, 384–409, 1953.
  • [15] M. Marianne, Rings of quotients of generalized matrix rings, Comm. Algebra, 15 (10), 1991–2015, 1987.
  • [16] W.K. Nicholson, Semiregular modules and rings, Canad. J. Math. 28 (5), 1105–1120, 1976.
  • [17] W.K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc. 229, 269-278, 1977.
  • [18] W.K. Nicholson, Strongly clean rings and Fittings lemma, Comm. Algebra, 27, 3583– 3592, 1999.
  • [19] S. Sahinkaya and T. Yildirim, UJ-endomorphism rings, The Mathematica Journal, 60 (83), 186–198, 2018.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

M. Tamer Koşan 0000-0002-5071-4568

Truong Cong Quynh 0000-0002-0845-0175

Tülay Yıldırım 0000-0002-7289-5064

Jan žemlička Bu kişi benim 0000-0003-3319-5193

Yayımlanma Tarihi 6 Ağustos 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 49 Sayı: 4

Kaynak Göster

APA Koşan, M. T., Quynh, T. C., Yıldırım, T., žemlička, J. (2020). Rings such that, for each unit u, u − u n belongs to the Jacobson radical. Hacettepe Journal of Mathematics and Statistics, 49(4), 1397-1404. https://doi.org/10.15672/hujms.542574
AMA Koşan MT, Quynh TC, Yıldırım T, žemlička J. Rings such that, for each unit u, u − u n belongs to the Jacobson radical. Hacettepe Journal of Mathematics and Statistics. Ağustos 2020;49(4):1397-1404. doi:10.15672/hujms.542574
Chicago Koşan, M. Tamer, Truong Cong Quynh, Tülay Yıldırım, ve Jan žemlička. “Rings Such That, for Each Unit U, U − U N Belongs to the Jacobson Radical”. Hacettepe Journal of Mathematics and Statistics 49, sy. 4 (Ağustos 2020): 1397-1404. https://doi.org/10.15672/hujms.542574.
EndNote Koşan MT, Quynh TC, Yıldırım T, žemlička J (01 Ağustos 2020) Rings such that, for each unit u, u − u n belongs to the Jacobson radical. Hacettepe Journal of Mathematics and Statistics 49 4 1397–1404.
IEEE M. T. Koşan, T. C. Quynh, T. Yıldırım, ve J. žemlička, “Rings such that, for each unit u, u − u n belongs to the Jacobson radical”, Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 4, ss. 1397–1404, 2020, doi: 10.15672/hujms.542574.
ISNAD Koşan, M. Tamer vd. “Rings Such That, for Each Unit U, U − U N Belongs to the Jacobson Radical”. Hacettepe Journal of Mathematics and Statistics 49/4 (Ağustos 2020), 1397-1404. https://doi.org/10.15672/hujms.542574.
JAMA Koşan MT, Quynh TC, Yıldırım T, žemlička J. Rings such that, for each unit u, u − u n belongs to the Jacobson radical. Hacettepe Journal of Mathematics and Statistics. 2020;49:1397–1404.
MLA Koşan, M. Tamer vd. “Rings Such That, for Each Unit U, U − U N Belongs to the Jacobson Radical”. Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 4, 2020, ss. 1397-04, doi:10.15672/hujms.542574.
Vancouver Koşan MT, Quynh TC, Yıldırım T, žemlička J. Rings such that, for each unit u, u − u n belongs to the Jacobson radical. Hacettepe Journal of Mathematics and Statistics. 2020;49(4):1397-404.

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