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Strongly clean matrix rings over noncommutative local rings

Li Bingjun
대한수학회 (The Korean Mathematical Society)|2009.01|대한수학회보 (Bulletin of the KMS)|제46권 제1호|pp. 71-78

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참고문헌

키워드

similaritymatrix ringstrongly clean ringlocal ring
주제분류수학

초록

An element of a ring R with identity is called strongly clean if it is the sum of an idempotent and a unit that commute, and R is called strongly clean if every element of R is strongly clean. Let R be a noncommutative local ring, a criterion in terms of solvability of a simple quadratic equation in R is obtained for M_2(R) to be strongly clean.

Abstract

An element of a ring R with identity is called strongly clean if it is the sum of an idempotent and a unit that commute, and R is called strongly clean if every element of R is strongly clean. Let R be a noncommutative local ring, a criterion in terms of solvability of a simple quadratic equation in R is obtained for M_2(R) to be strongly clean.

참고문헌 (13)

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  7. T. J. Dorsey, "Cleanness and Strong Cleanness of Rings of Matrices", pp.2006
  8. J. Han, "Extensions of clean rings", Comm. Algebra, 29(6), pp.2589~2595 (2001)
  9. T. Y. Lam, "A First Course in Noncommutative Rings" (1991), Springer-Verlag
  10. Y. Li, "Strongly clean matrix rings over local rings", J. Algebra, 312(1), pp.397~404 (2007)
  11. W. K. Nicholson, "Lifting idempotents and exchange rings", Trans. Amer. Math. Soc., 229, pp.269~278 (1977)
  12. W. K. Nicholson, "Strongly clean rings and Fitting's lemma", Comm. Algebra, 27(8), pp.3583~3592 (1999)
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관련 논문AI추천

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