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A Module M is called cofinite J- Supplemented Module if for every cofinite submodule L of M, there exists a submodule N of M such that M=L+N with main properties of cof-J-supplemented modules. An R-module M is called fully invariant-J-supplemented if for every fully invariant submodule N of M, there exists a submodule K of M, such that M = N + K with N K K. A condition under which the direct sum of FI-J-supplemented modules is FI-J-supplemented was given. Also, some types of modules that are related to the FI-J-supplemented module were discussed.

Let R be an associative ring with identity and let M be a left R-module . As a generalization of µ-semiregular modules, we introduce an F-µ-semiregular module. Let F be a submodule of M and x∊M. x is called F-µ-semiregular element in M , if there exists a decomposition M=A⨁B, such that A is a projective submodule of and . M is called F-µ-semiregular if x is F-µ-semiregular element for each x∊M. A condition under which the module µ-semiregular is F-µ-semiregular module was given. The basic properties and some characterizations of the F-µ-semiregular module were provided.

Let be a commutative ring with an identity and be a unitary -module. We say that a non-zero submodule of is primary if for each with en either or and an -module is a small primary if = for each proper submodule small in. We provided and demonstrated some of the characterizations and features of these types of submodules (modules).

We introduce in this paper, the notion of a 2-quasì-prime module as a generalization of quasi-prime module, we know that a module E over a ring R is called quasi-prime module, if (0) is quasi-prime submodule. Now, we say that a module E over ring R is a 2-quasi-prime module if (0) is 2-quasi-prime submodule, a proper submodule K of E is 2-quasi-prime submodule if whenever , and , then either or .
Many results about these kinds of modules are obtained and proved, also, we will give a characterization of these kinds of modules.

In this paper, we introduce a type of modules, namely S-K-nonsingular modules, which is a generalization of K-nonsingular modules. A comprehensive study of these classes of modules is given.

Zur Weiterbildung für Richtmeister in der Stahlbaumontage wurden Module in Form von Lernaufgaben entwickelt, die zusammen ein Lernaufgabensystem ergeben. Die Lernaufgaben decken das komplette Berufswissen ab, das für die Lösung einer Arbeitsaufgabe gezielt abgefordert werden kann. Alle Lernaufgaben entsprechen vollständigen Arbeitsaufträgen der Stahlbaumontage. Neben der Wissensaneignung werden strukturelle Kompetenzen der Aufgabenlösung und Problembewältigung angeeignet. Jede Lernaufgabe wird als "Polar" dargestellt, das ihren Schwierigkeitsgrad bewertet und so eine Einschätzung der Aufgabe ermöglicht. Die entwickelten Elemente stellen Vorarbeiten für die Integration zu einem schlüssigen Bildungsgang auf dem Weg zum allgemein anerkannten Qualifikationsziel "Richtmeister" dar. (BIBB)

In this paper, we introduce and study the notions of fuzzy quotient module, fuzzy (simple, semisimple) module and fuzzy maximal submodule. Also, we give many basic properties about these notions.

Fuchs introduced purely extending modules as a generalization of extending modules. Ahmed and Abbas gave another generalization for extending modules named semi-extending modules. In this paper, two generalizations of the extending modules are combined to give another generalization. This generalization is said to be almost semi-extending. In fact, the purely extending modules lies between the extending and almost semi-extending modules. We also show that an almost semi-extending module is a proper generalization of purely extending. In addition, various examples and important properties of this class of modules are given and considered. Another characterization of almost semi-extending modules is established. Moreover, the relationships with other related concepts are studied and discussed

Throughout this note, R is commutative ring with identity and M is a unitary R-module. In this paper, we introduce the concept of quasi J- submodules as a – and give some of its basic properties. Using this concept, we define the class of quasi J-regular modules, where an R-module J- module if every submodule of is quasi J-pure. Many results about this concept

Throughout this work we introduce the notion of Annihilator-closed submodules, and we give some basic properties of this concept. We also introduce a generalization for the Extending modules, namely Annihilator-extending modules. Some fundamental properties are presented as well as we discuss the relation between this concept and some other related concepts.

In this work, we introduce a new generalization of both Rationally extending and Goldie extending which is Goldie Rationally extending module which is known as follows: if for any submodule K of an R-module M there is a direct summand U of M (denoted by U⊆_⊕ M) such that K β_r U. A β_r is a relation of K⊆M and U⊆M, which defined as K β_r U if and only if K ⋂U⊆_r K and K⋂U⊆_r U.

Modularity is a fundamental doctrine in the cognitive sciences. It holds a preeminent position in cognitive psychology and generative linguistics, as well as a long history in neurophysiology, with roots going all the way back to the early nineteenth century. But a mature field of neuroscience is a comparatively recent phenomenon and has challenged orthodox conceptions of the modular mind. One way of accommodating modularity within the new framework suggested by these developments is to go for increasingly soft versions of modularity. One such version, which I call the "system" view, is so soft that it promises to meet practically any challenge neuroscience can throw at it. In this paper, I reconsider afresh what we ought to regard as the sine qua non of modularity and offer a few arguments against the view that an insipid "system" module could be the legitimate successor of the traditional notion. ; This research was supported by an Australian Government Research Training Program (RTP) Scholarship.

A procura pela redução do consumo e dos custos de energia, nas organizações, levou à implementação de sistemas de gestão de energia, que numa primeira fase possibilitou a monitorização automática dos consumos. Contudo, consequência de obrigatoriedades legais, da redução de custos e de políticas energéticas de consciencialização ambiental, existe uma procura crescente de ferramentas, integradas nos sistemas de gestão, que auxiliem a atingir os objetivos de melhoria da eficiência energética. Em particular, a recente norma 50001, muito focada na eficiência energética, conta com número crescente de empresas que procuram certificar os seus sistemas de gestão de energia de acordo com esta norma.Nesse sentido, este projeto de dissertação pretende analisar as soluções existentes no mercado, idealizar e especificar um módulo de gestão de energia compatível com a norma, que permita gerir a energia de acordo com os seus requisitos, examinando os principais consumos, criando planos de melhoria e avaliando os seus resultados. Posteriormente, e ainda no âmbito desta dissertação, será desenvolvida uma parte do módulo 50001 de forma a validar os conceitos, a especificação e a arquitetura idealizada. ; The search of energy consumption and cost reductions, in organizations, led to the implementation of energy management systems, that allowed automatic consumption monitoring. However, consequence of the harsher legislation, the search for cost reduction and the energy policies focused on the environment protection, there is a growing demand for tools, integrated in management systems, that support the pursuit of energy efficiency improvement goals.In this sense, this master dissertation project intends to perform an analysis of the current available market solutions, the idealization and specification of a management module compatible with the standard, that allows for main energy uses examination according to the norm, creating improvement plans and evaluating their results. Finally, within the context of this dissertation, part of the 50001 module will be developed so that the concepts, specification and architecture can be validated.

We introduce in this paper the concept of an approximately pure submodule as a generalization of a pure submodule, that is defined by Anderson and Fuller. If every submodule of an R-module is approximately pure, then is called F-approximately regular. Further, many results about this concept are given.

The three volumes cover the essential themes of macroeconomics included in an undergraduate program of study. Each volume deals with one year of study or a single modular unit. The volumes build on each other thematically, but are designed to be used independently, so each volume can be read alone. The updated new edition has been expanded to include a chapter on prosperity indicators.