Characterizations of normal elements in rings with involution

Qu, Yunyun; Wei, Junchao; Yao, Hua

doi:10.1007/s10474-018-0874-z

Cited by 15 publications

(11 citation statements)

References 3 publications

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“…By Theorem 1.1, we have aR = aa * R = (a # ) * a * R ⊆ (a # ) * R = a * R = a † R, this means that a † = a # . Thus a is normal and a † = a * by (5).…”

Section: Characterizations Of Normal Elementsmentioning

confidence: 99%

“…By [5,Lemma 2.7], we have a ∈ R EP , which gives a = a 2 a † . By [5, Corollary 2.8], we get (a † ) * a † = a † (a † ) * .…”

Section: Characterizations Of Normal Elementsmentioning

confidence: 99%

“…Let a ∈ R † ∩ R # . Then a is normal if and only if the following equation (5) has at least one solution in χ a .…”

Section: Characterizations Of Normal Elementsmentioning

confidence: 99%

“…The following results are frequently used in this paper. THEOREM 1.1 [5]. For any a ∈ R # ∩ R † , the following are satisfied:…”

Section: Introductionmentioning

confidence: 97%

“…It is known by [5, Corollary 2.8, Lemma 2.7] a ∈ R † is normal if and only if a † (a † ) * = (a † ) * a † or a ∈ R EP and a * a † = a † a * . More results on normal elements are given in [5].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Some new characterizations of normal elements

Shi

Weiaz

2019

Filomat

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“…By Theorem 1.1, we have aR = aa * R = (a # ) * a * R ⊆ (a # ) * R = a * R = a † R, this means that a † = a # . Thus a is normal and a † = a * by (5).…”

Section: Characterizations Of Normal Elementsmentioning

confidence: 99%

“…By [5,Lemma 2.7], we have a ∈ R EP , which gives a = a 2 a † . By [5, Corollary 2.8], we get (a † ) * a † = a † (a † ) * .…”

Section: Characterizations Of Normal Elementsmentioning

confidence: 99%

“…Let a ∈ R † ∩ R # . Then a is normal if and only if the following equation (5) has at least one solution in χ a .…”

Section: Characterizations Of Normal Elementsmentioning

confidence: 99%

“…The following results are frequently used in this paper. THEOREM 1.1 [5]. For any a ∈ R # ∩ R † , the following are satisfied:…”

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Some new characterizations of normal elements

Shi

Weiaz

2019

Filomat

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On G-Drazin partial order in rings

Dolinar,

Kuzma,

Marovt

et al. 2024

Acta Math. Hungar.

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We extend the concept of a G-Drazin inverse from the set $$M_n$$ M n of all $$n\times n$$ n × n complex matrices to the set $$\mathcal{R}^{D}$$ R D of all Drazin invertible elements in a ring $$\mathcal{R}$$ R with identity. We also generalize a partial order induced by G-Drazin inverses from $$M_n$$ M n to the set of all regular elements in $$\mathcal{R}^{D}$$ R D , study its properties, compare it to known partial orders, and generalize some known results.

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