Öz
ARis the sum of a unit and a projection that commute with each other. Inthis paper, we explore strong -cleanness of rings of continuous functions overspectrum spaces. We prove that a -ring R is strongly -clean if and only if Ris an abelian exchange ring and C(X) C (X) is-clean, if and only if R isan abelian exchange ring and the classical ring of quotients q(C(X)) of C(X)is -clean, where X is a spectrum space of R
Anahtar Kelimeler
Strongly -clean ring ring of continuous functions topological -space
Kaynakça
- F. Azarpanah, When is C(X) a clean ring?, Acta Math. Hungar. 94(2002), 53–58.
- S.K. Berberian, Baer -Rings, Springer-Verlag, Heidelberg, London, New York, 2011. H. Chen
- Rings Related Stable Range Conditions, Series in Algebra 11, World Scienti…c, Hackensack, NJ, 2011.
- H. Chen, A. Harmancı, A.Ç. Özcan, Strongly J -clean rings with involutions, Ring Theory gioR. López-Permouth, ,http://dx.doi.org/10.1090/conm/609/12091. Edited by
- S. TariqRizvi andCosmin Van Huynh, S. Roman, (609)(2014),123
- L. Gillman and M. Jerison, Rings of Continuous Functions, Springer-Verlag, New York, Heidelberg, Berlin, London, 1976.
- A.W. Hager, C.M. Kimber, Clean rings of continuous functions, Algebra Universalis 56(2007), –92.
- M.L. Knox, R. Levy, W.W. McGovern, J. Shapiro, Generalizations of complemented rings with applications to rings of functions, J. Algebra Appl. 8(2009), 17-40.
- C. Li, Y. Zhou, On strongly -clean rings, J. Algebra Appl. 10(2011), 1363-1370.
- K. Varadarajan, Study of Hop…city in certain classes of rings, Comm. Algebra 28(2000), 783.
- G.D. Marco, A. Orsatti, Commutative rings in which every prime ideal is contained in a unique maximal ideal, Proc. Amer. Math. Soc. 30 (1971), 459–466.
- W.W. McGovern, Clean semiprime f -rings with bounded inversion, Comm. Algebra (2003), 3295-3304.
- W.W. McGovern, Neat rings, J. Pure Appl. Algebra 205(2006), 243-265.
- A.A. Tuganbaev, Rings Close to Regular, Kluwer Academic Publishers, Dordrecht, Boston, London, 2002.
- L. Vas, -Clean rings; some clean and almost clean Baer -rings and von Neumann algebras, J. Algebra 324(2010), 3388-3400.
Öz
Kaynakça
- F. Azarpanah, When is C(X) a clean ring?, Acta Math. Hungar. 94(2002), 53–58.
- S.K. Berberian, Baer -Rings, Springer-Verlag, Heidelberg, London, New York, 2011. H. Chen
- Rings Related Stable Range Conditions, Series in Algebra 11, World Scienti…c, Hackensack, NJ, 2011.
- H. Chen, A. Harmancı, A.Ç. Özcan, Strongly J -clean rings with involutions, Ring Theory gioR. López-Permouth, ,http://dx.doi.org/10.1090/conm/609/12091. Edited by
- S. TariqRizvi andCosmin Van Huynh, S. Roman, (609)(2014),123
- L. Gillman and M. Jerison, Rings of Continuous Functions, Springer-Verlag, New York, Heidelberg, Berlin, London, 1976.
- A.W. Hager, C.M. Kimber, Clean rings of continuous functions, Algebra Universalis 56(2007), –92.
- M.L. Knox, R. Levy, W.W. McGovern, J. Shapiro, Generalizations of complemented rings with applications to rings of functions, J. Algebra Appl. 8(2009), 17-40.
- C. Li, Y. Zhou, On strongly -clean rings, J. Algebra Appl. 10(2011), 1363-1370.
- K. Varadarajan, Study of Hop…city in certain classes of rings, Comm. Algebra 28(2000), 783.
- G.D. Marco, A. Orsatti, Commutative rings in which every prime ideal is contained in a unique maximal ideal, Proc. Amer. Math. Soc. 30 (1971), 459–466.
- W.W. McGovern, Clean semiprime f -rings with bounded inversion, Comm. Algebra (2003), 3295-3304.
- W.W. McGovern, Neat rings, J. Pure Appl. Algebra 205(2006), 243-265.
- A.A. Tuganbaev, Rings Close to Regular, Kluwer Academic Publishers, Dordrecht, Boston, London, 2002.
- L. Vas, -Clean rings; some clean and almost clean Baer -rings and von Neumann algebras, J. Algebra 324(2010), 3388-3400.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Bölüm | Research Article |
| Yazarlar | |
| Yayımlanma Tarihi | 1 Şubat 2018 |
| Yayımlandığı Sayı | Yıl 2018 Cilt: 67 Sayı: 1 |
Kaynak Göster
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
