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Generalized Inverses and Solutions to Equations in Rings with Involution

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In this paper, we focus on partial isometry elements and strongly EP elements or a ring. We construct characterizing equations such that an element which both group invertible and MP-invertible, is a partial isometry element, or is strongly EP, exactly when these equations have solution in a given set.

Abstract

In this paper, we focus on partial isometry elements and strongly EP elements or a ring. We construct characterizing equations such that an element which both group invertible and MP-invertible, is a partial isometry element, or is strongly EP, exactly when these equations have solution in a given set.

참고문헌 (15)

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  3. R. E. Hartwig, "Block generalized inverses", Arch. Rational Mech. Anal., 61, pp.197~251 (1976)
  4. S. Karanasios, "EP elements in rings and semigroup with involution and C*-algebras", Serdica Math. J., 41, pp.83~116 (2015)
  5. J. J. Koliha, "Elements of rings with equal spectral idempotents", J. Aust. Math. Soc, 72(1), pp.137~152 (2002)
  6. D. Mosi´c, "Moore-Penrose-invertible normal and Hermitian elements in rings", Linear Algebra Appl., 431, pp.732~745 (2009)
  7. D. Mosi´c, "Partial isometries and EP elements in rings with involution", Electron. J. Linear Algebra, 18, pp.761~772 (2009)
  8. D. Mosi´c, "Further results on partial isometries and EP elements in rings with involution", Math. Comput. Modelling, 54(1-2), pp.460~465 (2011)
  9. D. Mosi´c, "EP elements in rings", Linear Algebra Appl., 431, pp.527~535 (2009)
  10. R. Penrose, "A generalized inverse for matrices", Proc. Cambridge Philos. Soc., 51, pp.406~413 (1955)
  11. Y. C. Qu, "Characterizations of normal elements in ring with involution", Acta. Math. Hungar., 156(2), pp.459~464 (2018)
  12. S. Z. Xu, "EP elements in rings with involution", Bull. Malay. Math. Soc. Ser., 42, pp.3409~3426 (2019)
  13. Z. C. Xu, "Strongly EP elements in a ring with involution", Filomat, 34(6), pp.2101~2107 (2020)
  14. R. J. Zhao, "Characterizations of partial isometries and two special kinds of EP elements", Czechoslovak Math. J., 70, pp.539~551 (2020)
  15. D. D. Zhao, "Strongly EP elements in rings with involution", J. Algebra Appl., 21(5), pp.2250088~ (2022)

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