In this paper, we give two new optimal parallel algorithms for MATRIX MULTIPLICATION which are designed to run on a Fibonacci hypercube structure. At first, we present a broadcast algorithm on Fibonacci hypercube with O (n) time complexity. We use this broadcast algorithm and algorithms presented by Gunnels, Lin, Morrow and Geijn on a mesh structure, in order to present two optimal parallel MATRIX MULTIPLICATION algorithms on a Fibonacci hypercube structure. We show these algorithms are cost-optimal. The performance of the algorithm has been tested on a simulative parallel system.

The objective of this study was to develop a new optimal parallel algorithm for MATRIX MULTIPLICATION which could run on a Fibonacci Hypercube structure. Most of the popular algorithms for parallel MATRIX MULTIPLICATION can not run on Fibonacci Hypercube structure, therefore giving a method that can be run on all structures especially Fibonacci Hypercube structure is necessary for parallel MATRIX MULTIPLICATION. For creating this method, a new model for MATRIX MULTIPLICATION with an algorithm for data distribution on Fibonacci Hypercube structure was provided. Other than this, another optimized algorithm was designed on Mesh structure. By running the algorithms on a simulative parallel system and giving the results in graphical mode, it has been found that these two algorithms have optimized value in parallel MATRIX MULTIPLICATION and they are more efficient than the previous algorithms.

In this paper we introduce the concept of MULTIPLICATION-like modules and we obtain some related results. We show that an R-module M is MULTIPLICATION-like if and only if for each ideal I of R, I = (IM: R M). We prove that any MULTIPLICATION-like module is faithful and r-MULTIPLICATION. So we get that any at and MULTIPLICATION-like module is faithfully at.

Let M be a lattice module over the multiplicative lattice L. An L-module M is called a MULTIPLICATION lattice module if for every element NÎM there exists an element aÎL such that N=a1M. Our objective is to investigate properties of prime elements of MULTIPLICATION lattice modules.