Generalized Zhou inverses in rings
نویسندگان
چکیده
We introduce and study a new class of generalized inverses in rings. An element ring R has Zhou inverse if there exists b∈R such that bab=b,b∈comm2(a),an−ab∈J(R) for some n∈N. We...
منابع مشابه
Generalized Inverses of a Sum in Rings
We study properties of the Drazin index of regular elements in a ring with a unity 1. We give expressions for generalized inverses of 1−ba in terms of generalized inverses of 1−ab. In our development we prove that the Drazin index of 1 − ba is equal to the Drazin index of 1 − ab. 2000 Mathematics subject classification. primary 15A09; secondary 16U99.
متن کاملPartial orders in rings based on generalized inverses – unified theory
Article history: Received 20 August 2014 Accepted 3 January 2015 Available online xxxx Submitted by Y. Wei MSC: 06A06 15A09 16U99
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Fredholm’s method to solve a particular integral equation in 1903, was probably the first written work on generalized inverses. In 1906, Moore formulated the generalized inverse of a matrix in an algebraic setting, which was published in 1920, and in the thirties von Neumann used generalized inverses in his studies of continuous geometries and regular rings. Kaplansky and Penrose, in 1955, inde...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2021
ISSN: ['1532-4125', '0092-7872']
DOI: https://doi.org/10.1080/00927872.2021.1914072