Tas an 𝒢 submodule ofG

Submodule Algebras

The complement operation on modules has not been argued so far as we know. We observe that it plays an important role in software maintenance, as well as join and meet operations. A de nition of a module and operations on them is given in category theoretic terms; we adopt well-known characterization of complement as a left adjoint to join. The de nition is rst given locally and then extended t...

On the Large Deviations Behaviour of Acyclic Networks ofG / G / 1 Queues 1

We consider a single class, acyclic network of G/G/1 queues. We impose some mild assumptions on the service and external arrival processes and we characterize the large deviations behaviour of all the processes resulting from various operations in the network. For the network model that we are considering, these operations are passing-through-asingle-server-queue (the process resulting from thi...

Submodule Construction Using Derivatives

Top-down design methodology is one of the widely used approaches to the design of complex concurrent systems. In this approach, the speciication of a system is decomposed into a set of submodules whose concurrent behavior is equivalent to that of the system speciication. The following problem is of particular importance when using this methodology: given the speciication of a system and some of...

A Simple Ordinal Recursive Normalization ofG odel

Small submodules with respect to an arbitrary submodule

Let $R$ be an arbitrary ring and $T$ be a submodule of an $R$-module $M$. A submodule $N$ of $M$ is called $T$-small in $M$ provided for each submodule $X$ of $M$, $Tsubseteq X+N$ implies that $Tsubseteq X$. We study this mentioned notion which is a generalization of the small submodules and we obtain some related results.