STRONGLY -CLEAN PROPERTIES AND RINGS OF FUNCTIONS

Huanyin Chen; Abdullah Harmancı

doi:10.1501/Commua1_0000000834

STRONGLY -CLEAN PROPERTIES AND RINGS OF FUNCTIONS

Year 2018, Volume: 67 Issue: 1, 102 - 115, 01.02.2018

Huanyin Chen Abdullah Harmancı

https://doi.org/10.1501/Commua1_0000000834

Abstract

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

Keywords

Strongly -clean ring, ring of continuous functions, topological -space

References

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.

Year 2018, Volume: 67 Issue: 1, 102 - 115, 01.02.2018

Huanyin Chen Abdullah Harmancı

https://doi.org/10.1501/Commua1_0000000834

Abstract

References

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.

There are 15 citations in total.

Details

Primary Language	English
Journal Section	Research Articles
Authors	Huanyin Chen This is me Abdullah Harmancı This is me
Publication Date	February 1, 2018
Published in Issue	Year 2018 Volume: 67 Issue: 1

Cite

APA	Chen, H., & Harmancı, A. (2018). STRONGLY -CLEAN PROPERTIES AND RINGS OF FUNCTIONS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 67(1), 102-115. https://doi.org/10.1501/Commua1_0000000834
AMA	Chen H, Harmancı A. STRONGLY -CLEAN PROPERTIES AND RINGS OF FUNCTIONS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2018;67(1):102-115. doi:10.1501/Commua1_0000000834
Chicago	Chen, Huanyin, and Abdullah Harmancı. “STRONGLY -CLEAN PROPERTIES AND RINGS OF FUNCTIONS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67, no. 1 (February 2018): 102-15. https://doi.org/10.1501/Commua1_0000000834.
EndNote	Chen H, Harmancı A (February 1, 2018) STRONGLY -CLEAN PROPERTIES AND RINGS OF FUNCTIONS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67 1 102–115.
IEEE	H. Chen and A. Harmancı, “STRONGLY -CLEAN PROPERTIES AND RINGS OF FUNCTIONS”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 67, no. 1, pp. 102–115, 2018, doi: 10.1501/Commua1_0000000834.
ISNAD	Chen, Huanyin - Harmancı, Abdullah. “STRONGLY -CLEAN PROPERTIES AND RINGS OF FUNCTIONS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67/1 (February 2018), 102-115. https://doi.org/10.1501/Commua1_0000000834.
JAMA	Chen H, Harmancı A. STRONGLY -CLEAN PROPERTIES AND RINGS OF FUNCTIONS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2018;67:102–115.
MLA	Chen, Huanyin and Abdullah Harmancı. “STRONGLY -CLEAN PROPERTIES AND RINGS OF FUNCTIONS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 67, no. 1, 2018, pp. 102-15, doi:10.1501/Commua1_0000000834.
Vancouver	Chen H, Harmancı A. STRONGLY -CLEAN PROPERTIES AND RINGS OF FUNCTIONS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2018;67(1):102-15.