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Communications in Algebra Volume 45, 2017 - Issue 6
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Original Articles

Elementary matrix reduction over certain rings

Marjan SheibaniFaculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran
,
Rahman BahmaniFaculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran
&
Huanyin ChenDepartment of Mathematics, Hangzhou Normal University, Hangzhou, ChinaCorrespondence[email protected]
Pages 2613-2618 | Received 23 Dec 2015, Published online: 07 Oct 2016

References

  • Anderson, D. D., Juett, J. R. (2012). Stable range and almost stable range. J. Pure Appl. Algebra 216:2094–2097.
  • Anderson, D. D., Winders, M. (2009). Idealization of a module. J. Commut. Algebra 1:3–56.
  • Anderson, D. F., Badawi, A. (2012). Von Neumann regular and related elements in commutative rings. Algebra Colloq. 19:1017–1040.
  • Bakkari, C. (2009). On P-Bézout rings. Int. J. Algebra 3:669–673.
  • Bass, H. (1964). K-Theory and stable algebra. Inst. Haut. Études Sci. Publ. Math. 22:5–60.
  • Chen, H. (2011). Rings Related Stable Range Conditions. Series in Algebra, Vol. 11. Hackensack, NJ: World Scientific.
  • Domsha, O. V., Vasiunyk, I. S. (2014). Combining local and adequate rings. In: Book of Abstracts of the International Algebraic Conference. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine, July 7–12, 2014.
  • Gillman, L., Henriksen, M. (1956). Rings of continuous functions in which every finitely generated ideal is principal. Trans. Am. Math. Soc. 82:366–391.
  • Gillman, L., Henriksen, M. (1956). Some remarks about elementary divisor rings. Trans. Am. Math. Soc. 82:362–365.
  • Henriksen, M. (1955). Some remarks on elementary divisor rings II. Michigan Math. J. 3:159–163.
  • Kaplansky, I. (1949). Elementary divisors and modules. Trans. Am. Math. Soc. 66:464–491.
  • McGovern, W. W. (2006). Neat rings. J. Pure Appl. Algebra 205:243–265.
  • McGovern, W. W. (2008). Bézout rings with almost stable range 1. J. Pure Appl. Algebra 212:340–348.
  • Roitman, M. (2013). The Kaplansky condition and rings of almost stable range 1. Proc. Am. Math. Soc. 141:3013–3018.
  • Zabavsky, B. V. (2003). Reduction of matrices over Bézout rings of stable rank not higher than 2. Ukrain. Math. J. 55:665–670.
  • Zabavsky, B. V. (2012). Diagonal Reduction of Matrices Over Rings. Mathematical Studies Monograph Series, Vol. XVI. Lviv, Ukraine: VNTL Publisher.
  • Zabavsky, B. V. (2014). Diagonal reduction of matrices over finite stable range rings. Math. Stud. 41:101–108.
  • Zabavsky, B. V., Bilavska, S. I. (2012). Every zero adequate ring is an exchange ring. J. Math. Sci. 187:153–156.
  • Zabavsky, B. V., Domsha, O. (2011). Diagonalizability theorem for matrices over certain domains. Algebra Discrete Math. 12:132–139.

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