2018
DOI: 10.2298/fil1809073g
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*-DMP elements in *-semigroups and *-rings

Abstract: 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; … Show more

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Cited by 20 publications
(5 citation statements)
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“…The symbols R (1,3) , R † , R D , R # , R P I , R # , R D , and R W denote the sets of all {1, 3}-invertible elements, Moore-Penrose invertible elements, Drazin invertible elements, group invertible elements, partial isometries, core invertible elements, pseudo core invertible elements, and weak group invertible elements, respectively, in the ring R. Lemma 2.2. [5] (Core-EP decomposition) Let a ∈ R. Then a ∈ R D if and only if a = a 1 + a 2 , for unique elements a 1 , a 2 ∈ R such that following conditions hold:…”
Section: Preliminariesmentioning
confidence: 99%
“…The symbols R (1,3) , R † , R D , R # , R P I , R # , R D , and R W denote the sets of all {1, 3}-invertible elements, Moore-Penrose invertible elements, Drazin invertible elements, group invertible elements, partial isometries, core invertible elements, pseudo core invertible elements, and weak group invertible elements, respectively, in the ring R. Lemma 2.2. [5] (Core-EP decomposition) Let a ∈ R. Then a ∈ R D if and only if a = a 1 + a 2 , for unique elements a 1 , a 2 ∈ R such that following conditions hold:…”
Section: Preliminariesmentioning
confidence: 99%
“…The notion of core-EP inverse for matrices was extended to elements of a ring with involution in [7] and generalized Drazin invertible operators on Hilbert space in [20]. For detailed results related to core-EP pre-orders, see [8,17,22].…”
Section: Introductionmentioning
confidence: 99%
“…AA † is an orthogonal projector onto R(A k ) and A † A is an oblique projector on to R(A k ) along N ((A k ) † A). The core inverse and core-EP inverse have applications in partial order theory (see for example, [8][9][10]).…”
Section: Introductionmentioning
confidence: 99%