논문KCI 등재
ON 2 × 2 STRONGLY CLEAN MATRICES
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초록
An element in a ring R is strongly clean provided that it is the sum of an idempotent and a unit that commutate. In this note, several necessary and sufficient conditions under which a 2×2 matrix over an integral domain is strongly clean are given. These show that strong cleanness over integral domains can be characterized by quadratic and Diophantine equations.
Abstract
An element in a ring R is strongly clean provided that it is the sum of an idempotent and a unit that commutate. In this note, several necessary and sufficient conditions under which a 2×2 matrix over an integral domain is strongly clean are given. These show that strong cleanness over integral domains can be characterized by quadratic and Diophantine equations.
참고문헌 (10)
- J. Chen, "On strongly clean matrix and triangular matrix rings", Comm. Algebra, 34(1), pp.3659~3674 (2006)
- H. Chen, "Rings Related Stable Range Conditions, Series in Algebra 11" (2011), World Scientific
- A. J. Diesl, "Classes of Strongly Clean Rings", 박사, pp.2006
- T. J. Dorsey, "Cleanness and Strong Cleanness of Rings of Matrices", 박사, pp.2006
- D. Khurana, "Clean matrices and unit-regular matrices", J. Algebra, 280(2), pp.683~698 (2004)
- Li Bingjun, "Strongly clean matrix rings over noncommutative local rings", 대한수학회보, 46(1), pp.71~78 (2009), 대한수학회
- W. K. Nicholson, "Strongly clean rings and Fitting’s lemma, Comm", Algebra, 27(8), pp.3583~3592 (1999)
- W. K. Nicholson, "Clean rings: a survey, Advances in ring theory", pp.181~198 (2005), World Sci. Publ.
- K. N. Rajeswari, "A note on clean matrices in M2(Z)", Int. J. Algebra, 3(5), pp.241~248 (2009)
- K. N. Rajeswari, "Strongly clean matrices in M2(Z) : an intrinsic characterization", Internat. J. Math. Arch, 2, pp.1159~1166 (2011)
관련 논문AI추천
Strongly clean matrix rings over noncommutative local ringsLi Bingjun대한수학회 · 대한수학회보2009 · 제46권 제1호Some strongly nil clean matrices over local ringsHuanyin Chen대한수학회 · 대한수학회보2011 · 제48권 제4호Strong J-cleanness of formal matrix ringsA. Harmanci, O. Gurgun, S. Halicioglu장전수학회 · Advanced Studies in Contemporary Mathematics2014 · 제24권 제4호Certain Clean Decompositions for Matrices over Local RingsHandan Kose, Huanyin Chen, Yosum Kurtulmaz경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2023 · 제63권 제4호STRONGLY NIL CLEAN MATRICES OVER R[x]/(x2 - 1)Huanyin Chen대한수학회 · 대한수학회보2012 · 제49권 제3호Strongly Clean Matrices Over Power SeriesHandan Kose, Huanyin Chen, Yosum Kurtulmaz경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제2호
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