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 matr...

 Let $R$ be a commutative ring with identity and $M$ be a finitely generated unital $R$-module. In this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. Moreover, we investigate some conditions which imply that the module $M$ is the direct sum of some cyclic modules and free modules. Then some properties of Fitting ideals o...

The standard references for this section are [Gro91], [Kol90] and [McC91]. Let E be an elliptic curve over Q of conductor N . Let K = Q( √ −D), where −D is a fundamental discriminant, D #= 3, 4, and all prime factors of N are split in K, i.e. (N) = NN̄ for an ideal N of the ring of integers OK of K with OK/N $ Z/NZ. We call such a discriminant a Heegner discriminant for E/Q. By the modularity th...

Let R be a commutative ring with unity. And let E unitary R-module. This paper introduces the notion of 2-prime submodules as generalized concept ideal, where proper submodule H module F over is said to if , for r and x implies that or . we prove many properties this kind submodules, then only [N ] E, R. Also, non-zero multiplication module, [K: F] [H: every k such K. Furthermore, will study ba...

Let E be an elliptic curve having Complex Multiplication by the ring OK of integers of K = Q( √−D), let H = K(j(E)) be the Hilbert class field of K. Then the Mordell-Weil group E(H) is an OK-module. Its Steinitz class St(E) is studied here. In particular, when D is a prime number, St(E) is determined: If D ≡ 3 (mod 4) then St(E) = 1; if D ≡ 1 (mod 4) then St(E) = [P]t, where P is any prime-idea...

It is a well known theorem that an abelian group G satisfying G = nG for every positive integer n is a direct summand of every abelian group H which contains G as a subgroup. It is the object of this note to generalize this theorem to abelian groups admitting a ring of operators, and to show that the corresponding conditions are not only sufficient but are at the same time necessary. Finally we...

Consider a zero-dimensional ideal I in K[X1, . . . ,Xn]. Inspired by Faugère and Mou’s Sparse FGLM algorithm, we use Krylov sequences based on multiplication matrices of I in order to compute a description of its zero set by means of univariate polynomials. Steel recently showed how to use Coppersmith’s block-Wiedemann algorithm in this context; he describes an algorithm that can be easily para...

H [n] = {(t1, . . . , tn) ∈ R n \ {0} | ∀j, [tj 6= 0 and t1 = t2 = · · · = tj−1 = 0] ⇒ tj > 0} ∪ {0}. LetM(H) denote the Banach algebra of all complex Borel measures with support contained in H, with the usual addition and scalar multiplication, and with convolution ∗, and the norm being the total variation of μ. It is shown that the maximal ideal space X(M(H)) of M(H), equipped with the Gelfan...

Certain non-associative algebras have important applications intheoretical Mendelian genetics. The following definitions and summary of the theory are taken from papers by Etherington [2]-[7], who initiated their study. A baric algebra is one which admits a non-trivial homomorphism, x-*a)(x), into its coefficient field. co(#) is called the weight of £. In this paper we shall only be concerned w...