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Clean integral 2 × 2 matrices are characterized. Up to similarity the strongly clean matrices are completely determined and large classes of uniquely clean matrices are found. In particular, classes of uniquely clean matrices which are not strongly clean are found.

  • [1]

    Alpern, D., Quadratic Equation Solver, www.alpertron.com.ar/quad.htm.

  • [2]

    Andrica, D. and Călugăreanu, G., A nil-clean 2 × 2 matrix over integers which is not clean, J. Algebra Appl., 13 (6), (2014), 9 pages.

    • Search Google Scholar
    • Export Citation
  • [3]

    Behn, A. and Van der Merwe, A. B., An algorithmic version of the theorem by Latimer and MacDuffee for 2 times 2 integral matrices, Linear Algebra Appl., 346 (2002), 114.

    • Search Google Scholar
    • Export Citation
  • [4]

    Andrica, D. and Călugăreanu, G., Uniquely clean 2 × 2 invertible integral ma-trices, Studia Univ. Babeş-Bolyai, 62 (3), (2017), 287293.

    • Search Google Scholar
    • Export Citation
  • [5]

    Călugăreanu, G. and Lam, T. Y., Fine rings: A new class of simple rings, J. Algebra Appl., 15 (9), (2016), 18 pages.

  • [6]

    Diesl, A. J., Classes of strongly clean rings, Ph. D. thesis, University of California, Berkeley (2006).

  • [7]

    Nicholson, W. K., Lifting idempotents and exchange rings, Trans. Amer. Math. Soc., 229 (1977), 269278.

  • [8]

    Nicholson, W. K. and Zhou, Y., Rings in which elements are uniquely the sum of an idempotent and a unit, Glasg. Math. J., 46 (2), (2004), 227236.

    • Search Google Scholar
    • Export Citation