Further results on partial isometries and EP elements in rings with involution

Mosić, Dijana; Djordjević, Dragan S.

doi:10.1016/j.mcm.2011.02.035

Cited by 36 publications

(21 citation statements)

References 9 publications

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“…D. Mosić and D.S. Djordjevć also characterize partial isometries in terms of the pure theory of rings, generalizing known results for complex matrices (see [22,23]). …”

mentioning

confidence: 76%

“…It should be noted that the Moore-Penrose inverse and the group inverse are useful in solving overdetermined systems of linear equations, and the importance of EP elements lies in the fact that they are characterized by the commutativity with their Moore-Penrose inverses. There are close connections among EP elements, partial isometries and normal elements in rings with involution (see [22,23]). …”

Section: Wx Chenmentioning

confidence: 99%

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

Chen¹

2012

ELA

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“…D. Mosić and D.S. Djordjevć also characterize partial isometries in terms of the pure theory of rings, generalizing known results for complex matrices (see [22,23]). …”

mentioning

confidence: 76%

Section: Wx Chenmentioning

confidence: 99%

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

Chen¹

2012

ELA

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“…Duo to [11], an element a of a * −ring R is said to be EP if a ∈ R ∩ R † and a = a † . In [10], many characterizations of EP elements are given.…”

Section: Generalized Inversesmentioning

confidence: 99%

NEC rings

Pan¹,

Li²,

Wei³

2018

Filomat

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A ring R is called NEC if for any a, b ∈ N(R), ab = ba. The class of NEC rings is a proper generalization of the class of CN rings. First, with the aid of NEC rings, some characterizations of CN rings and reduced rings are given. Next we extend many properties of CN rings to NEC rings such as we show that NEC rings are directly finite and left min-abel; NEC regular ring are strongly regular ; a ring R is NEC if and only if every Pierce stalk of R is NEC; Also we discuss some properties of NEC exchange rings; Finally, we give some properities of MP-invertible elements. 2010 Mathematics Subject Classification. 16E50 16D30 16B99 Keywords. NEC ring; reduced ring; clean ring; exchange ring; quasi-normal ring; regular ring; Moore penrose inverse; EP element.

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“…An element a ∈ R † is called a partial isometry [11] if a * = a † . We denote by R PI the set of all the partial isometries of R. Partial isometries has been explored by many authors.…”

Section: Introductionmentioning

confidence: 99%