호남수학학술지 (Honam Mathematical Journal)

  • 제41권2호
  • /
  • Pages.321-328
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  • 2019
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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RINGS WHOSE ELEMENTS ARE SUMS OF FOUR COMMUTING IDEMPOTENTS

  • 투고 : 2018.10.17
  • 심사 : 2018.12.29
  • 발행 : 2019.06.25
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초록

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).

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참고문헌

  1. P.V. Danchev, Invo-clean unital rings, Commun. Korean Math. Soc. 32(1) (2017), 19-27. https://doi.org/10.4134/CKMS.C160054
  2. P.V. Danchev, Weakly invo-clean unital rings, Afr. Mat. 28(7-8) (2017), 1285-1295. https://doi.org/10.1007/s13370-017-0515-7
  3. P.V. Danchev, Feebly invo-clean unital rings, Ann. Univ. Sci. Budapest (Sect. Math.) 60 (2017), 85-91.
  4. P.V. Danchev, A generalization of fine rings, Palest. J. Math. 7(2) (2018), 425-429.
  5. P.V. Danchev, A note on fine WUU rings, Palest. J. Math. 7(2) (2018), 430-431.
  6. 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.
  7. P.V. Danchev, Rings whose elements are represented by at most three commuting idempotents, Gulf J. Math. 6(2) (2018), 1-6.
  8. 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. https://doi.org/10.1007/s41980-018-0113-y
  9. P.V. Danchev, Rings whose elements are sums or minus sums of two commuting idempotents, Boll. Un. Mat. Ital. 12(3) (2019).
  10. 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.
  11. Y. Hirano and H. Tominaga, Rings in which every element is the sum of two idempotents, Bull. Austral. Math. Soc. 37 (1988), 161-164. https://doi.org/10.1017/S000497270002668X
  12. T.Y. Lam, A First Course in Noncommutative Rings, Second Edition, Graduate Texts in Math., Vol. 131, Springer-Verlag, Berlin-Heidelberg-New York, 2001.
  13. 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. https://doi.org/10.1080/03081087.2017.1417969
  14. 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. https://doi.org/10.4153/CMB-2016-009-0