Products of EP elements in reflexive semigroups

Hartwig, Robert E.; Katz, Irving J.

doi:10.1016/0024-3795(76)90058-6

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2024

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Cited by 22 publications

(4 citation statements)

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“…It is known by [10,Theorem 7.3] that a ∈ R is EP if and only if a is group invertible and aa # is symmetric. More results on EP elements can also be found in [2,4,5,7,11,15].…”

Section: Introductionmentioning

confidence: 91%

EP elements and the solutions of equation in rings with involution

Zhao¹,

Yao²,

Wei³

2018

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“…It is known by [10,Theorem 7.3] that a ∈ R is EP if and only if a is group invertible and aa # is symmetric. More results on EP elements can also be found in [2,4,5,7,11,15].…”

Section: Introductionmentioning

confidence: 91%

EP elements and the solutions of equation in rings with involution

Zhao¹,

Yao²,

Wei³

2018

Filomat

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“…As a matter of convenience, we use the terminology EP element instead of *-gMP element in this paper. Many authors have published papers on EP elements, see [2,3,7,8,9,12] for example. In particular, Xu, Chen and Bentítez [12] said that a ∈ R is an EP element if and only if there exists x ∈ R such that (1.5) xa 2 = a, ax 2 = x and (xa) * = xa.…”

Section: Introductionmentioning

confidence: 99%

New results on EP elements in rings with involution

Wang

Mosić²,

Gao³

2020

Preprint

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“…2 Characterizations of *-DMP elements EP elements are widely investigated in * -semigroups and * -rings ( see [3], [4], [9], [10], [14], [15], [18]). In this section, we give several characterizations of *-DMP elements.…”

Section: Introductionmentioning

confidence: 99%

-DMP elements in -semigroups and *-rings

Gao¹,

Chen²,

Ke³

2018

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In this paper, we investigate *-DMP elements in * -semigroups and * -rings.The notion of *-DMP element was introduced by Patrício in 2004. An element a is *-DMP if there exists a positive integer m such that a m is EP. We first characterize *-DMP elements in terms of the {1,3}-inverse, Drazin inverse and pseudo core inverse, respectively. Then, we give the pseudo core decomposition utilizing the pseudo core inverse, which extends the core-EP decomposition introduced by Wang for matrices to an arbitrary *ring; and this decomposition turns to be a useful tool to characterize *-DMP elements. Further, we extend Wang's core-EP order from matrices to * -rings and use it to investigate *-DMP elements. Finally, we give necessary and sufficient conditions for two elements a, b in * -rings to have aa D = bb D , which contribute to investigate *-DMP elements.

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Products of EP elements in reflexive semigroups

Cited by 22 publications

References 7 publications

EP elements and the solutions of equation in rings with involution

EP elements and the solutions of equation in rings with involution

New results on EP elements in rings with involution

-DMP elements in -semigroups and *-rings

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Products of EP elements in reflexive semigroups

Cited by 22 publications

References 7 publications

EP elements and the solutions of equation in rings with involution

EP elements and the solutions of equation in rings with involution

New results on EP elements in rings with involution

*-DMP elements in *-semigroups and *-rings

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-DMP elements in -semigroups and *-rings