Since the beginning of the 21st century, we observe rapid changes in the area of, broadly understood, computational sciences. One of interesting effects of these changes is the need for reevaluation of the role of dense matrix multiplication. The aim of this paper is two-fold. First, to summarize developments that point toward a need for reconsidering usefulness of matrix multiplication generalized on the basis of the theory of algebraic semirings. Second, to propose generalized matrix-matrix multiply-and-update (MMU) operation and its object oriented model.