Elements of rings with equal spectral idempotents

By Jerry J. Koliha, Pedro Patrício. Journal of the Australian Mathematical Society, 2002

190 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Polymers and Plastics

View Paper: https://www.semanticscholar.org/paper/ceb736d07215b6bf0e85706da8b09f3357fdb6c7

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In Algebra and Number Theory

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Citations in the corpus

On generalized inverses and Green's relations (2009, background): “1, we then get directly the following existence criteria and commuting relations for the classical inverses [4], [2], [5], [6], [7], [8], [14], [9]:”
Moore–Penrose inverse in rings with involution (2007, methodology): “The paper is motivated by the work of Harte and Mbekhta [11,12] in C∗-algebras and Koliha and Patricio [18] in rings with involution.”
GENERALIZED INVERSES OF A SUM IN RINGS (2010, background): “In [5] the authors give the following characterization of EP elements in a ring.”
Jacobson’s lemma for the generalized Drazin inverse (2012, background): “Following Koliha and Patricio [15], the commutant and double commutant of an element a ∈ R are defined by comm(a) = {x ∈ R : ax = xa}; comm2(a) = {x ∈ R : xy = yx for all y ∈ comm(a)}, respectively.”
Pseudo Drazin inverses in associative rings and Banach algebras (2012, background): “a ∈ R is g-Drazin invertible if there exists b ∈ comm(2)(a) such that ab(2) = b and a(2)b − a ∈ R (see [17]), denoted by a ∈ R (that is, a is quasipolar).”
Outer Generalized Inverses in Rings (2005, background): “In the case when a ∈ , where is a C∗-algebra, the element a exists if and only if there exists some c ∈ such that aca = a (Harte and Mbekhta, 1992; Koliha and Patricio, 2002).”
Pseudo core inverses in rings with involution (2016, background): “It is well known that a ∈ RD if and only if ak ∈ R# for some positive integer k [10]; a ∈ RD if and only if ak ∈ RD for arbitrary positive integer k if and only if ak ∈ RD for some positive integer k [4]; if a ∈ RD, then aD ∈ RD with (aD)D = a2aD [4].”