Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Generalized Core Inverse in a proper $*$-ring (2005.13782v3)

Published 28 May 2020 in math.RA

Abstract: In this paper, we introduce the notion of weak core and central weak core inverse in a {\it proper $$-ring}. We further elaborate on these two classes by producing a few representations and characterizations of the weak core and central weak core invertible elements. We investigated additive properties and a few explicit expressions for these two classes of inverses through other generalized inverses. In addition, numerical examples are provided to validate claims on weak core inverses. Following {\it proper $$-ring} and their interconnections with Clifford algebra, we also present examples of the group inverse and the weak core inverse of a non-zero non-invertible quaternion $\mathbb{H}_s$.

Summary

We haven't generated a summary for this paper yet.