a module $m$ is said to be coretractable if there exists a nonzero homomorphism of every nonzero factor of $m$ into $m$. we prove that all right (left) modules over a ring are coretractable if and only if the ring is morita equivalent to a finite product of local right and left perfect rings.

10. Galois modules and class field theory Boas Erez In this section we shall try to present the reader with a sample of several significant instances where, on the way to proving results in Galois module theory, one is lead to use class field theory. Conversely, some contributions of Galois module theory to class fields theory are hinted at. We shall also single out some problems that in our op...

Abstract : In this paper, we propose an architecture that performs both forward and inverse lifting−based discrete wavelet transform. Our architecture reduces the hardware requirement by exploiting the redundancy in the arithmetic operation involved in DWT computation. The proposed architecture does not require any extra memory to store intermediate results. The proposed architecture consists o...

KEGG, Kyoto Encyclopedia of Genes and Genomes, project consists of three types of data, pathways, hierarchies, and binary relations, that are used to represent biological knowledge. We present here a C++ library for e cient calculation of possible pathways from binary relations. In practice, the library is used to calculate metabolic pathways from the substrate-product relations of enzymes stor...

Recently, Mark Jones introduced first class structures as a means to express modular structure. In this paper we elaborate on this idea by comparing the module systems of Standard ML and Haskell 1.3, two widely used functional languages, and a Haskell variant equipped with such first class structures. Moreover, we look at another obvious and well-known extension to Hindley-Milner type systems, ...

criticism of public extension services has resulted in various countries seeking alternative approaches for provision of these services. in all these approaches, extension personnel are the key factors to the success of the implementation. today, agricultural extension services in turkey bear the responsibility of the ministry of food, agriculture and livestock. a number of non-public extension...

Several proof-assistants rely on the very formal basis of Pure Type Systems (PTS) as their foundations. We are concerned with the issues involved in the development of large proofs in these provers such as namespace management, development of reusable proof libraries and separate verification. Although implementations offer many features to address them, few theoretical foundations have been la...

LF has been designed and successfully used as a meta-logical framework to represent and reason about object logics. Here we design a representation of the Isabelle logical framework in LF using the recently introduced module system for LF. The major novelty of our approach is that we can naturally represent the advanced Isabelle features of type classes and locales. Our representation of type c...

As an extension of Bayesian Network, Module Network is good for dealing with problems where there are many variables but only a small set of data available. However it’s still time-consuming to learn a Module Network. In this paper, we propose a parallel implementation of the Module Network learning algorithm based on the message passing model. In order to solve the load-imbalance problem intro...

Let F be a local non-Archimedean field with ring of integers o and uniformizer ̟. Let X be a one-dimensional formal o-module of F -height n over the algebraic closure F of the residue field of o. By the work of Drinfeld, the universal deformation X of X is a formal group over a power series ring R0 in n − 1 variables over the completion of the maximal unramified extension ônr of o. For h ∈ {0, ....