대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제34권4호
  • /
  • Pages.1069-1078
  • /
  • 2019
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

STRONG P-CLEANNESS OF TRIVIAL MORITA CONTEXTS

  • 투고 : 2018.08.26
  • 심사 : 2018.12.05
  • 발행 : 2019.10.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Let R be a ring with identity and P(R) denote the prime radical of R. An element r of a ring R is called strongly P-clean, if there exists an idempotent e such that $r-e=p{\in}P$(R) with ep = pe. In this paper, we determine necessary and sufficient conditions for an element of a trivial Morita context to be strongly P-clean.

키워드

참고문헌

  1. G. Borooah, A. J. Diesl, and T. J. Dorsey, Strongly clean triangular matrix rings over local rings, J. Algebra 312 (2007), no. 2, 773-797. https://doi.org/10.1016/j.jalgebra.2006.10.029
  2. G. Borooah, A. J. Diesl, and T. J. Dorsey, Strongly clean matrix rings over commutative local rings, J. Pure Appl. Algebra 212 (2008), no. 1, 281-296. https://doi.org/10.1016/j.jpaa.2007.05.020
  3. M. B. Calci, S. Halicioglu, A. Harmanci, and B. Ungor, Prime Structures in a Morita Context, http://arxiv.org/abs/1812.02920.
  4. H. Chen, On 2 $\times$ 2 strongly clean matrices, Bull. Korean Math. Soc. 50 (2013), no. 1, 125-134. https://doi.org/10.4134/BKMS.2013.50.1.125
  5. H. Chen, H. Kose, and Y. Kurtulmaz, Strongly P-clean rings and matrices, Int. Electron. J. Algebra 15 (2014), 116-131. https://doi.org/10.24330/ieja.266242
  6. J. Chen, X. Yang, and Y. Zhou, When is the 2$\times$2 matrix ring over a commutative local ring strongly clean?, J. Algebra 301 (2006), no. 1, 280-293. https://doi.org/10.1016/j.jalgebra.2005.08.005
  7. J. Chen, X. Yang, and Y. Zhou, On strongly clean matrix and triangular matrix rings, Comm. Algebra 34 (2006), no. 10, 3659-3674. https://doi.org/10.1080/00927870600860791
  8. A. J. Diesl, Nil clean rings, J. Algebra 383 (2013), 197-211. https://doi.org/10.1016/j.jalgebra.2013.02.020
  9. I. Kaplansky, Topological representation of algebras. II, Trans. Amer. Math. Soc. 68 (1950), 62-75. https://doi.org/10.2307/1990539
  10. Y. Li, Strongly clean matrix rings over local rings, J. Algebra 312 (2007), no. 1, 397-404. https://doi.org/10.1016/j.jalgebra.2006.10.032
  11. K. Morita, Duality for modules and its applications to the theory of rings with minimum condition, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 6 (1958), 83-142.
  12. M. Muller, Rings of quotients of generalized matrix rings, Comm. Algebra 15 (1987), no. 10, 1991-2015. https://doi.org/10.1080/00927878708823519
  13. W. K. Nicholson, Strongly clean rings and Fitting's lemma, Comm. Algebra 27 (1999), no. 8, 3583-3592. https://doi.org/10.1080/00927879908826649
  14. G. Song and X. Guo, Diagonability of idempotent matrices over noncommutative rings, Linear Algebra Appl. 297 (1999), no. 1-3, 1-7. https://doi.org/10.1016/S0024-3795(99)00059-2
  15. G. Tang, C. Li, and Y. Zhou, Study of Morita contexts, Comm. Algebra 42 (2014), no. 4, 1668-1681. https://doi.org/10.1080/00927872.2012.748327
  16. G. Tang and Y. Zhou, Strong cleanness of generalized matrix rings over a local ring, Linear Algebra Appl. 437 (2012), no. 10, 2546-2559. https://doi.org/10.1016/j.laa.2012.06.035