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Drazin–Moore–Penrose invertibility in rings

✍ Scribed by Pedro Patrı́cio; Roland Puystjens

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
223 KB
Volume
389
Category
Article
ISSN
0024-3795

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✦ Synopsis

Characterizations are given for elements in an arbitrary ring with involution, having a group inverse and a Moore-Penrose inverse that are equal and the difference between these elements and EP-elements is explained. The results are also generalized to elements for which a power has a Moore-Penrose inverse and a group inverse that are equal.

As an application we consider the ring of square matrices of order m over a projective free ring R with involution such that R m is a module of finite length, providing a new characterization for range-Hermitian matrices over the complexes.

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In this paper we present several new characterizations of normal and Hermitian elements in rings with involution in purely algebraic terms, and considerably simplify proofs of already existing characterizations.

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✍ R. Puystjens; M.C. Gouveia 📂 Article 📅 2004 🏛 Elsevier Science 🌐 English ⚖ 190 KB

Characterizations are given for existence of the Drazin inverse of a matrix over an arbitrary ring. Moreover, the Drazin inverse of a product P AQ for which there exist a P and Q such that P P A = A = AQQ can be characterized and computed. This generalizes recent results obtained for the group inver