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Certain Clean Decompositions for Matrices over Local Rings

Handan Kose|Huanyin Chen|Yosum Kurtulmaz
경북대학교 자연과학대학 수학과|2023.12|Kyungpook Mathematical Journal|제63권 제4호|pp. 561-569|DOI https://doi.org/10.5666/KMJ.2023.63.4.561

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키워드

Local ringStrongly clean matrixStrongly rad-clean matrixPower-series
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초록

An element a ∈ R is strongly rad-clean provided that there exists an idem potent e ∈ R such that a-e ∈ U(R), ae = ea and eae ∈ J(eRe). In this article, we completely determine when a 2x2 matrix over a commutative local ring is strongly rad clean. An application to matrices over power-series is also given.

Abstract

An element a ∈ R is strongly rad-clean provided that there exists an idem potent e ∈ R such that a-e ∈ U(R), ae = ea and eae ∈ J(eRe). In this article, we completely determine when a 2x2 matrix over a commutative local ring is strongly rad clean. An application to matrices over power-series is also given.

참고문헌 (11)

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  3. S. Breaz, "Matrices over nite elds as sums of periodic and nilpotent elements", Linear Algebra Appl, 555, pp.92~97 (2018)
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  5. J. Cui, "When is a matrix ring over a commutative local ring quasipolar?", Comm. Algebra, 39(9), pp.3212~3221 (2011)
  6. P. Danchev, "Certain properties of square matrices over elds with applications to rings", Rev. Colombiana Mat, 54(2), pp.109~116 (2020)
  7. P. Danchev, "Decompositions of matrices into potent and square-zero matrices", Internat. J. Algebra Comput, 32(2), pp.251~263 (2022)
  8. A. J. Diesl, "Strongly clean matrices over arbitrary rings", J. Algebra, 399, pp.854~869 (2014)
  9. Y. Li, "Strongly clean matrix rings over local rings", J. Algebra, 312(1), pp.397~404 (2007)
  10. J. Ster, "On expressing matrices over Z2 as the sum of an idempotent and a nilpotent", Linear Algebra Appl, 544(10), pp.339~349 (2018)
  11. G. Tang, "Matrices over a commutative ring as sums of three idempotents or three involutions", Linear Multilinear Algebra, 67(2), pp.267~277 (2019)

관련 논문AI추천

Strongly Clean Matrices Over Power SeriesHandan Kose, Huanyin Chen, Yosum Kurtulmaz경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제2호Some 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 제4호STRONGLY NIL CLEAN MATRICES OVER R[x]/(x2 - 1)Huanyin Chen대한수학회 · 대한수학회보2012 · 제49권 제3호Strongly clean matrix rings over noncommutative local ringsLi Bingjun대한수학회 · 대한수학회보2009 · 제46권 제1호Quasipolar matrix rings over local ringsJian Cui, Xiaobin Yin대한수학회 · 대한수학회보2014 · 제51권 제3호

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