대한수학회지 (Journal of the Korean Mathematical Society)

  • 제47권1호
  • /
  • Pages.1-15
  • /
  • 2010
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

ON QUASI-STABLE EXCHANGE IDEALS

  • Chen, Huanyin (Department of Mathematics Hangzhou Normal University)
  • 발행 : 2010.01.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

We introduce, in this article, the quasi-stable exchange ideal for associative rings. If I is a quasi-stable exchange ideal of a ring R, then so is $M_n$(I) as an ideal of $M_n$(R). As an application, we prove that every square regular matrix over quasi-stable exchange ideal admits a diagonal reduction by quasi invertible matrices. Examples of such ideals are given as well.

키워드

참고문헌

  1. P. Ara, Extensions of exchange rings, J. Algebra 197 (1997), no. 2, 409-423 https://doi.org/10.1006/jabr.1997.7116
  2. P. Ara, K. R. Goodearl, K. C. O'Meara, and E. Pardo, Diagonalization of matrices over regular rings, Linear Algebra Appl. 265 (1997), 147-163 https://doi.org/10.1016/S0024-3795(96)00596-4
  3. H. Chen, Elements in one-sided unit regular rings, Comm. Algebra 25 (1997), no. 8, 2517-2529 https://doi.org/10.1080/00927879708826002
  4. H. Chen, Generalized stable regular rings, Comm. Algebra 31 (2003), no. 10, 4899-4910 https://doi.org/10.1081/AGB-120023138
  5. H. Chen, 2 × 2 invertible matrices over weakly stable rings, J. Korean Math. Soc. 46 (2009), no. 2, 257-269 https://doi.org/10.4134/JKMS.2009.46.2.257
  6. H. Chen and M. Chen, Generalized ideal-stable regular rings, Comm. Algebra 31 (2003), no. 10, 4989-5001 https://doi.org/10.1081/AGB-120023143
  7. H. Chen and M. Chen, On products of three triangular matrices over associative rings, Linear Algebra Appl. 387 (2004), 297-311 https://doi.org/10.1016/j.laa.2004.01.023
  8. K. R. Goodearl, Von Neumann Regular Rings, Pitman, London, San Francisco, Melbourne, 1979; second ed., Krieger, Malabar, Fl., 1991
  9. T. Y. Lam, A crash course on stable range, cancellation, substitution and exchange, J. Algebra Appl. 3 (2004), no. 3, 301-343 https://doi.org/10.1142/S0219498804000897
  10. D. Lu, Q. Li, and W. Tong, Comparability, stability, and completions of ideals, Comm. Algebra 32 (2004), no. 7, 2617–2634 https://doi.org/10.1081/AGB-120037403
  11. K. C. O'Meara and R. Raphael, Uniform diagonalisation of matrices over regular rings, Algebra Universalis 45 (2000), 383-405 https://doi.org/10.1007/s000120050221
  12. F. Perera, Lifting units modulo exchange ideals and $C^*$-algebras with real rank zero, J. Reine Angew. Math. 522 (2000), 51-62 https://doi.org/10.1515/crll.2000.040