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Let be a commutative ring with identity, and be a unitary left R-module. In this paper we, introduce and study a new class of modules called pure hollow (Pr-hollow) and pure-lifting (Pr-lifting). We give a fundamental, properties of these concept. also, we, introduce some conditions under which the quotient and direct sum of Pr-lifting modules is Pr-lifting.

Aus der Gegenüberstellung der europäischen und der nationalen Dimension der modularen Berufsausbildung nimmt der Verfasser eine Positionsbestimmung vor. Für einen Teil der EU-Mitgliedstaaten stellen Module einen wichtigen ersten Schritt zum Aufbau oder einen Ansatz zur Weiterentwicklung ihres nationalen Bildungssystems dar. In Deutschland sollte grundsätzlich an einer auf dem Berufskonzept basierenden dualen Ausbildung festgehalten werden. Das duale System vermittelt auf der Grundlage eines klar definierten Ausbildungsberufs eine Berufsqualifizierung mit Abschluß. Module können diese Transparenz nicht herstellen; sie sollten als Zusatzqualifikationen in der Weiterbildung und für bestimmte Zielgruppen bedarfsorientiert ausgebaut werden. (BIBB)

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Let be an associative ring with identity and let be a unitary left -module. Let be a non-zero submodule of .We say that is a semi- - hollow module if for every submodule of such that is a semi- - small submodule ( ). In addition, we say that is a semi- - lifting module if for every submodule of , there exists a direct summand of and such that
The main purpose of this work was to develop the properties of these classes of module.

Let be a commutative ring with 1 and be a left unitary . In this paper, the generalizations for the notions of compressible module and retractable module are given.
An is termed to be semi-essentially compressible if can be embedded in every of a non-zero semi-essential submodules. An is termed a semi-essentially retractable module, if for every non-zero semi-essentially submodule of an . Some of their advantages characterizations and examples are given. We also study the relation between these classes and some other classes of modules.

We introduce the notion of t-polyform modules. The class of t- polyform modules contains the class of polyform modules and contains the class of t-essential quasi-Dedekind.
Many characterizations of t-polyform modules are given. Also many connections between these class of modules and other types of modules are introduced.

This paper aims to introduce the concepts of -closed, -coclosed, and -extending modules as generalizations of the closed, coclossed, and extending modules, respectively. We will prove some properties as when the image of the e*-closed submodule is also e*-closed and when the submodule of the e*-extending module is e*-extending. Under isomorphism, the e*-extending modules are closed. We will study the quotient of e*-closed and e*-extending, the direct sum of e*-closed, and the direct sum of e*-extending.

In this paper, we introduce the notion of a 2-prime module as a generalization of prime module E over a ring R, where E is said to be prime module if (0) is a prime submodule. We introduced the concept of the 2-prime R-module. Module E is said to be 2-prime if (0) is 2-prime submodule of E. where a proper submodule K of module E is 2-prime submodule if, whenever rR, xE, E, Thus xK or [K: E].

Gangyong Lee, S.Tariq Rizvi, and Cosmin S.Roman studied Rickart modules.
The main purpose of this paper is to develop the properties of Rickart modules .
We prove that each injective and prime module is a Rickart module. And we give characterizations of some kind of rings in term of Rickart modules.

In this paper, as generalization of second modules we introduce type of modules namely (essentially second modules). A comprehensive study of this class of modules is given, also many results concerned with this type and other related modules presented.