Abstract
In this paper, some characterizations of partial isometries, normal elements and strongly $EP$ elements are given by the construction of $EP$ elements. At the same time, the partial isometry elements are characterized by the existence of solutions of equations in rings in a given set, and also by the general form of solutions of given equations.
Keywords
Group inverse MP-invertible element partial isometry element $EP$ element strongly $EP$ element normal element
References
- A. Ben-Israel and T. N. E Greville, Generalized Inverses: Theory and Applications, 2nd. ed., Springer, New York, 2003.
- S. Karanasios, EP elements in rings and semigroup with involution and $C^*$-algebras, Serdica Math. J., 41 (2015), 83-116.
- J. J. Koliha and P. Patricio, Elements of rings with equal spectral idempotents, J. Aust. Math. Soc., 72 (2002), 137-152.
- D. Mosic and D. S. Djordjevic, Partial isometries and EP elements in rings with involution, Electron. J. Linear Algebra, 18 (2009), 761-772.
- D. Mosic and D. S. Djordjevic, Further results on partial isometries and EP elements in rings with involution, Math. Comput. Modelling, 54 (2011), 460- 465.
- D. Mosic, D. S. Djordjevic and J. J. Koliha, EP elements in rings, Linear Algebra Appl., 431 (2009), 527-535.
- Y. C. Qu, J. C. Wei and H. Yao, Characterizations of normal elements in rings with involution, Acta. Math. Hungar., 156(2) (2018), 459-464.
- Z. C. Xu, R. J. Tang and J. C. Wei, Strongly EP elements in a ring with involution, Filomat, 34(6) (2020), 2101-2107.
- S. Z. Xu, J. L. Chen and J. Benítez, EP elements in rings with involution, Bull. Malays. Math. Sci. Soc., 42 (2019), 3409-3426.
- R. J. Zhao, H. Yao and J. C. Wei, Characterizations of partial isometries and two special kinds of EP elements, Czechoslovak Math. J., 70(145) (2020), 539- 551.
- R. J. Zhao, H. Yao and J. C. Wei, EP elements and the solutions of equation in rings with involution, Filomat, 32(13) (2018), 4537-4542.
Abstract
References
- A. Ben-Israel and T. N. E Greville, Generalized Inverses: Theory and Applications, 2nd. ed., Springer, New York, 2003.
- S. Karanasios, EP elements in rings and semigroup with involution and $C^*$-algebras, Serdica Math. J., 41 (2015), 83-116.
- J. J. Koliha and P. Patricio, Elements of rings with equal spectral idempotents, J. Aust. Math. Soc., 72 (2002), 137-152.
- D. Mosic and D. S. Djordjevic, Partial isometries and EP elements in rings with involution, Electron. J. Linear Algebra, 18 (2009), 761-772.
- D. Mosic and D. S. Djordjevic, Further results on partial isometries and EP elements in rings with involution, Math. Comput. Modelling, 54 (2011), 460- 465.
- D. Mosic, D. S. Djordjevic and J. J. Koliha, EP elements in rings, Linear Algebra Appl., 431 (2009), 527-535.
- Y. C. Qu, J. C. Wei and H. Yao, Characterizations of normal elements in rings with involution, Acta. Math. Hungar., 156(2) (2018), 459-464.
- Z. C. Xu, R. J. Tang and J. C. Wei, Strongly EP elements in a ring with involution, Filomat, 34(6) (2020), 2101-2107.
- S. Z. Xu, J. L. Chen and J. Benítez, EP elements in rings with involution, Bull. Malays. Math. Sci. Soc., 42 (2019), 3409-3426.
- R. J. Zhao, H. Yao and J. C. Wei, Characterizations of partial isometries and two special kinds of EP elements, Czechoslovak Math. J., 70(145) (2020), 539- 551.
- R. J. Zhao, H. Yao and J. C. Wei, EP elements and the solutions of equation in rings with involution, Filomat, 32(13) (2018), 4537-4542.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Publication Date | July 17, 2021 |
| DOI | https://doi.org/10.24330/ieja.969942 |
| IZ | https://izlik.org/JA77NK86FR |
| Published in Issue | Year 2021 Volume: 30 Issue: 30 |