Von-Neumann regular Q-Algebras and Q-Digraphs

Abstract

This study presents the notions of Von-Neumann regular Q-algebra and Q-digraph. Given a Q-algebra X, the corresponding graph, indicated by G ( )  , is a directed graph with vertices that correspond to elements of X. For two different elements a, b ∈ X, an Arc from a to b (written as a → b) exists if and only if a ∆ b = 0, where a ∆ b = (b ∗ a) ∗ a. We elaborate these ideas and offer examples. The paper also, analyze the Q-algebra (n ; ,0 - ) and indicates that it is a left Von-Neumann regular Q-algebra. In addition, features of the Q-digraph corresponding to the Q-algebra (n ; ,0 - ) will be examined. The main conclusion of this research is that the digraph linked. The principal finding of this paper will shed light on the digraph associated with ( ) 1 4.2 n- forms a tree digraph for all n ≥ 1.