2012
DOI: 10.13001/1081-3810.1540
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On EP elements, normal elements and partial isometries in rings with involution

Abstract: Abstract. This is a continuation to the study of EP elements, normal elements and partial isometries in rings with involution. The aim of this paper is to give the negative solution to three conjectures on this subject. Moreover, some new characterizations of EP elements in rings with involution are presented.

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Cited by 23 publications
(18 citation statements)
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References 24 publications
(29 reference statements)
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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%
“…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%
“…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%
“…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%