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http://dx.doi.org/10.5831/HMJ.2019.41.2.321

RINGS WHOSE ELEMENTS ARE SUMS OF FOUR COMMUTING IDEMPOTENTS  

Danchev, Peter Vassilev (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences)
Publication Information
Honam Mathematical Journal / v.41, no.2, 2019 , pp. 321-328 More about this Journal
Abstract
We completely characterize the isomorphic class of those associative unitary rings whose elements are sums of four commuting idempotents. Our main theorem enlarges results due to Hirano-Tominaga (Bull. Austral. Math. Soc., 1988), Tang et al. (Lin. & Multilin. Algebra, 2019), Ying et al. (Can. Math. Bull., 2016) as well as results due to the author in (Alban. J. Math., 2018), (Gulf J. Math., 2018), (Bull. Iran. Math. Soc., 2018) and (Boll. Un. Mat. Ital., 2019).
Keywords
rings; idempotents; finite fields;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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1 P.V. Danchev, Invo-clean unital rings, Commun. Korean Math. Soc. 32(1) (2017), 19-27.   DOI
2 P.V. Danchev, Weakly invo-clean unital rings, Afr. Mat. 28(7-8) (2017), 1285-1295.   DOI
3 Y. Hirano and H. Tominaga, Rings in which every element is the sum of two idempotents, Bull. Austral. Math. Soc. 37 (1988), 161-164.   DOI
4 T.Y. Lam, A First Course in Noncommutative Rings, Second Edition, Graduate Texts in Math., Vol. 131, Springer-Verlag, Berlin-Heidelberg-New York, 2001.
5 G. Tang, Y. Zhou and H. Su, Matrices over a commutative ring as sums of three idempotents or three involutions, Lin. and Multilin. Algebra 67(2) (2019), 267-277.   DOI
6 Z. Ying, T. Kosan and Y. Zhou, Rings in which every element is a sum of two tripotents, Can. Math. Bull. 59(3) (2016), 661-672.   DOI
7 P.V. Danchev, Feebly invo-clean unital rings, Ann. Univ. Sci. Budapest (Sect. Math.) 60 (2017), 85-91.
8 P.V. Danchev, A generalization of fine rings, Palest. J. Math. 7(2) (2018), 425-429.
9 P.V. Danchev, A note on fine WUU rings, Palest. J. Math. 7(2) (2018), 430-431.
10 P.V. Danchev, Rings whose elements are sums of three or minus sums of two commuting idempotents, Alban. J. Math. 12(1) (2018), 3-7.
11 P.V. Danchev, Rings whose elements are represented by at most three commuting idempotents, Gulf J. Math. 6(2) (2018), 1-6.
12 P.V. Danchev, Rings whose elements are sums of three or difference of two commuting idempotents, Bull. Iran. Math. Soc. 44(6) (2018), 1641-1651.   DOI
13 P.V. Danchev, Rings whose elements are sums or minus sums of two commuting idempotents, Boll. Un. Mat. Ital. 12(3) (2019).
14 P.V. Danchev and E. Nasibi, The idempotent sum number and n-thin unital rings, Ann. Univ. Sci. Budapest (Sect. Math.) 59 (2016), 85-98.