On f-clean rings and f-clean elements
DOI:
https://doi.org/10.4067/S0716-09172011000200010Keywords:
Full elements, f-Clean rings, Skew Hurwitz series.Abstract
An associative ring R with identity is called f-clean ring if every element in R is the sum of an idempotent and a full element. In this paper, various basic properties of f-clean rings and f-clean elements are proved. Also, we give some new charaterizations of f-clean rings. In addition, we prove that the ring of skew Hurwitz series T = (HR, σ) where σ is an automorphism of R is f-clean if and only if R is f-clean.
References
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[2] B. Li and L. Feng, f-Clean rings and rings having many full elements, J. Korean Math. Soc, 47, No. 2, pp. 247-261, (2010).
[3] J. Han and W.K. Nicholson, Extensions of clean rings, Comm. Algebra 29, pp. 2589—2595, (2001).
[4] P. Ara, K. R. Goodearl, and E. Pardo, K0of purely infinite simple regular rings, K-Theory 26, No. 1, pp. 69-100, (2002).
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[6] W. K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc., 229, pp. 278 - 279, (1977).
[7] W. K. Nicholson, Strongly clean rings and Fitting’s lemma, Comm. Algebra, 27, pp. 3583—3592, (1999).
[8] W. K. Nicholson, K. Varadarajan, Y. Zhou, Clean endomorphism rings, Arch. Math. (Basel) 83, No. 4, pp. 340—343, (2004).
[9] W. K. Nicholson and Y. Zhou, Clean general rings, Journal of Algebra, 291, pp. 297-311, (2005).
[2] B. Li and L. Feng, f-Clean rings and rings having many full elements, J. Korean Math. Soc, 47, No. 2, pp. 247-261, (2010).
[3] J. Han and W.K. Nicholson, Extensions of clean rings, Comm. Algebra 29, pp. 2589—2595, (2001).
[4] P. Ara, K. R. Goodearl, and E. Pardo, K0of purely infinite simple regular rings, K-Theory 26, No. 1, pp. 69-100, (2002).
[5] V. P. Camillo and H. P. Yu, Exchange rings, units and idempotents, Comm. Algebra 22, No. 12, pp. 4737-4749, (1994).
[6] W. K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc., 229, pp. 278 - 279, (1977).
[7] W. K. Nicholson, Strongly clean rings and Fitting’s lemma, Comm. Algebra, 27, pp. 3583—3592, (1999).
[8] W. K. Nicholson, K. Varadarajan, Y. Zhou, Clean endomorphism rings, Arch. Math. (Basel) 83, No. 4, pp. 340—343, (2004).
[9] W. K. Nicholson and Y. Zhou, Clean general rings, Journal of Algebra, 291, pp. 297-311, (2005).
Published
2011-12-09
How to Cite
[1]
A. H. Handam, “On f-clean rings and f-clean elements”, Proyecciones (Antofagasta, On line), vol. 30, no. 2, pp. 277-284, Dec. 2011.
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