Invertibility of multiplication modules All rings are commutative with 1 and all modules are unital. Let R be a ring and M an R-module. M is called multiplication if for each submodule N of M, N=IM for some ideal I of R. Multiplication modules have recently received considerable attention during the last twenty years. In this talk we give the de nition of invertible submodules as a natural gene...

Insulin stimulates a 2-fold increase in the amount of tyrosine aminotransferase and a 5-10-fold increase in the rate of amino acid transport in dexamethasone-treated rat hepatoma cells. In order to determine whether these effects are mediated by insulin receptors or receptors for insulin-like growth factors, we have examined the binding of 125I-labeled insulin and 125I-labeled multiplication-st...

A dedicated, non-symbolic, system yielding imprecise representations of large quantities (Approximate Number System, or ANS) has been shown to support arithmetic calculations of addition and subtraction. In the present study, 5-7-year-old children without formal schooling in multiplication and division were given a task requiring a scalar transformation of large approximate numerosities, presen...

By considering the notion of multiplication modules over a commutative ring with identity, first we introduce the notion product of two submodules of such modules. Then we use this notion to characterize the prime submodules of a multiplication module. Finally, we state and prove a version of Nakayama lemma for multiplication modules and find some related basic results. 1. Introduction. Let R b...

we state several conditions under which comultiplication and weak comultiplication modulesare cyclic and study strong comultiplication modules and comultiplication rings. in particular,we will show that every faithful weak comultiplication module having a maximal submoduleover a reduced ring with a finite indecomposable decomposition is cyclic. also we show that if m is an strong comultiplicati...

The division relation plays a prominent role throughout this note, and so, we start by presenting some of its basic properties and their relation to addition and multiplication. First, it is re exive because multiplication has a unit (i.e., m= 1×m) and it is transitive, since multiplication is associative. It is also (almost) preserved by linear combination because multiplication distributes ov...

It is essential that students develop fluency in basic multiplication during grades three through five, in order to achieve mastery of elementary arithmetic. Instruction during these grades is typically focused on teaching students multiplication facts via drills and rote memorization so they are able to quickly retrieve answers to multiplication facts. If automaticity of multiplication facts i...

This paper presents rhotrix multiplication and introduces its implementation on process grid topologies. Covered in this work, are reviews of generalization cases of n-dimensional rhotrix multiplication. A parallel program based on MPI master-worker paradigm is implemented. By means of analyzing the time complexity and memory requirement for the method, the authors provided insight into how to ...

In this paper we present a new method for fast scalar multiplication on el-liptic curves over GF (p) in FPGA using Edwards and twisted Edwards curves over GF (p 3). The presented solution works for curves with prime group order (for example for all NIST curves over GF (p)). It is possible because of using 2-isogenous twisted Edwards curves over GF (p 3) instead of using short Weierstrass curves...

A generalization of recent group-theoretic matrix multiplication algorithms to an analogue of the theory of partial matrix multiplication is presented. We demonstrate that the added flexibility of this approach can in some cases improve upper bounds on the exponent of matrix multiplication yielded by group-theoretic full matrix multiplication. The group theory behind our partial matrix multipli...