Extensions of $\mathcal{G}$-Based Matrix Partial Orders

Shorted Operators Relative to a Partial Order in a Regular Ring

“…Various partial orders on an abstract ring or on the ring of matrices over the real and complex numbers have been introduced by several authors either as an abstract study of questions in algebra, or for the study of problems in engineering and statistics (See, e.g. [1], [2], [4], [7], [12], and [13]). Also, a partial order on semigroups is studied by several authors (See, e.g.…”

Solutions of minus partial ordering equations over von Neumann regular rings

“…That is, any solution of (2) can be represented by (16) and (17). Thus (16) and (17) are the general solutions of (2).…”