On EP elements, normal elements and partial isometries in rings with involution

Chen, Weixing

doi:10.13001/1081-3810.1540

Cited by 23 publications

(18 citation statements)

References 24 publications

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“…In [9, Theorem 2.1], Mosić and Djordjević proved that a ∈ R EP if and only if a ∈ R # ∩R † and a n a † = a † a n for some n 1. This result also can be found in [5,Theorem 2.4] by Chen. In the following theorem, we give a generalization of this result.…”

supporting

confidence: 79%

EP Elements in Rings with Involution

Chen

Benítez

2019

Bull. Malays. Math. Sci. Soc.

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Let R be a unital ring with involution. We first show that the EP elements in R can be characterized by three equations. Namely, let a ∈ R, then a is EP if and only if there exists x ∈ R such that (xa) * = xa, xa 2 = a and ax 2 = x. Any EP element in R is core invertible and Moore-Penrose invertible. We give more equivalent conditions for a core (Moore-Penrose) invertible element to be an EP element. Finally, any EP element is characterized in terms of the n-EP property, which is a generalization of the bi-EP property.

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supporting

confidence: 79%

EP Elements in Rings with Involution

Chen

Benítez

2019

Bull. Malays. Math. Sci. Soc.

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“…By aa • = 0, we have a ∈ a(a * a) n R, that is the condition (3) in Theorem 3.1 is satisfied. By the equivalence between (1), (2) and 3and Lemma 2.6, which implies the equivalence between (1), (4) and (5). The equivalence between (1), (6)-(9) is similar to the equivalence between (1), (2)- (5).…”

Section: Resultsmentioning

confidence: 66%

“…In [2], Chen showed that the equivalent conditions such that a ∈ R to be an EP element are closely related with powers of the group and Moore-Penrose inverse of a. In [12], Mosić and Djordjević presented several equivalent conditions, which ensure that an element a ∈ R is a partial isometry and EP.…”

Section: Introductionmentioning

confidence: 99%

The Moore-Penrose inverse in rings with involution

Chen

2019

Filomat

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Let R be a unital ring with involution. In this paper, we first show that for an element a ∈ R, a is Moore-Penrose invertible if and only if a is well-supported if and only if a is co-supported. Moreover, several new necessary and sufficient conditions for the existence of the Moore-Penrose inverse of an element in a ring R are obtained. In addition, the formulae of the Moore-Penrose inverse of an element in a ring are presented.

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“…Recently, the EP elements are investigated in the context of rings with involution. For a recent account of the theory see, for example, [5], [11] and the references given there. (ii) a ∈ R † and p a = r a .…”

Section: Characterizations Of Ep Elementsmentioning

confidence: 99%