References
- Ehrlich, G. (1968). Unit-regular rings. Portugal. Math. 27:209–212.
- Gouveia, M. C., Puystjens, R. (1991). About the group inverse and the Moore-Penrose inverse of a product. Linear Algebra Appl. 150:361–369. DOI: https://doi.org/10.1016/0024-3795(91)90180-5.
- Hartwig, R. E., Shoaf, J. (1977). Group inverses and Drazin inverses of bidiagonal and triangular Toeplitz matrices. J. Aust. Math. Soc. 24(1):10–34. DOI: https://doi.org/10.1017/S1446788700020036.
- Jacobson, N. (1956). Structure of Rings, American Mathematical Society, Colloquium Publications, Vol. 37. Providence, RI: American Mathematical Society.
- Khurana, D., Lam, T. Y., Nielsen, P. (2017). Exchange elements in rings, and the equation XA−BX=I. Trans. Amer. Math. Soc. 369:495–516.
- Khurana, D., Lam, T. Y., Nielsen, P., Šter, J. (2020). Special clean elements in rings. J. Algebra Appl. 19(11):2050208. DOI: https://doi.org/10.1142/S0219498820502084.
- Monk, G. S. (1972). A characterization of exchange rings. Proc. Amer. Math. Soc. 35(2):349–353. DOI: https://doi.org/10.1090/S0002-9939-1972-0302695-2.
- Nicholson, W. K. (1977). Lifting idempotents and exchange rings. Trans. Amer. Math. Soc. 229:269–278. DOI: https://doi.org/10.1090/S0002-9947-1977-0439876-2.
- Nicholson, W. K. (1997). On exchange rings. Commun. Algebra 25(6):1917–1918. DOI: https://doi.org/10.1080/00927879708825962.
- Nicholson, W. K. (1999). Strongly clean rings and fitting’s lemma. Commun. Algebra 27(8):3583–3592. DOI: https://doi.org/10.1080/00927879908826649.
- Patrício, P., Mendes Araújo, C. (2010). Moore-Penrose inverse in involutory rings: the case aa†=bb†. Linear Multilinear Algebra. 58:445–452.
- Penrose, R. (1955). A generalized inverse for matrices. Math. Proc. Camb. Phil. Soc. 51(3):406–413. DOI: https://doi.org/10.1017/S0305004100030401.
- Puystjens, R., Hartwig, R. E. (1997). The group inverse of a companion matrix. Linear Multilinear Algebra. 43(1-3):137–150. DOI: https://doi.org/10.1080/03081089708818521.
- Sylvester, J. J. (1884). Sur l’equations en matrices px = xq. C. R. Acad. Sci. Paris. 99:67–71.
- Vaš, L. (2010). *-clean rings; some clean and almost clean Baer *-rings and von Neumann algebras. J. Algebra 324:3388–3400.
- Zhu, H. H., Chen, J. L., Patrício, P. (2016). Further results on the inverse along an element in semigroups and rings. Linear Multilinear Algebra 64(3):393–403. DOI: https://doi.org/10.1080/03081087.2015.1043716.
- Zhu, H. H., Chen, J. L., Patrício, P., Mary, X. (2017). Centralizer’s applications to the inverse along an element. Appl. Math. Comput. 315:27–33. DOI: https://doi.org/10.1016/j.amc.2017.07.046.