Geodesic
Some characterizations of strongly partial isometry elements in rings with involutions
Filomat, Tome 36 (2022) no. 3, p. 843

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DOI

In this paper, we study an element which is both group invertible and Moore Penrose invertible to be EP, partial isometry and strongly EP by discussing the existence of solutions in a definite set of some given constructive equations. Mainly, let a ∈ R # ∩ R +. Then we firstly show that an element a ∈ R EP if and only if and Equation : axa + + a + ax = 2x has at least one solution in χ a = {a, a # , a + , a * , (a #) * , (a +) * }. Next, a ∈ R SEP if and only if Equation: axa * + a + ax = 2x has at least one solution in χ a. Finally, a ∈ R PI if and only if Equation: aya * x = xy has at least one solution in ρ 2 a , where ρ a = {a, a # , a + , (a #) * , (a +) * }
DOI : 10.2298/FIL2203843Z
Classification : 15A09, 16U99, 16W10
Keywords: partial isometry, EP element, solutions of equation 
Shiyin Zhao; Junchao Wei. Some characterizations of strongly partial isometry elements in rings with involutions. Filomat, Tome 36 (2022) no. 3, p. 843 . doi: 10.2298/FIL2203843Z
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     author = {Shiyin Zhao and Junchao Wei},
     title = {Some characterizations of strongly partial isometry elements in rings with involutions},
     journal = {Filomat},
     pages = {843 },
     year = {2022},
     volume = {36},
     number = {3},
     doi = {10.2298/FIL2203843Z},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2203843Z/}
}
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