M is viewed as a right module over an arbitrary ring R with identity. The essential second modules is defined in this paper. We call M is essential second when for any a bilongs to R, either Ma = 0 or Ma <e M. Number of conclusions are gained and some connections between these modules and other related modules are studied.
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Abstract This research deals with the definition of the concept of nodal purposes, And what is related to it, from its aim and importance, And for the purposes of the importance of Streptococcus In trying to understand the nodal truths For different minds, Especially with those who object to the introduction of belief in purposes studies, This research has two requirements: The first requirement: the concept and the aim of contractual purposes,It consists of two branches, The first is in the concept of nodal purposes, And it dealt with the definitions in terms of language and terminology And what we see is proportional to what aim |
This paper depends on sheding some litgt on the characteristics of political
relations between the arab and the Persian during the reign of sassane kings.
"Ardashir the first, shahbour the first, shahbour the second, Bahram the fifth; kisra
Anushrwan and kisrah abruis"
And who rulled the Persian before the Islamic conquest and were adopted in this studym
as a model. It was possible to get some information from invaluable refereces in order to
arrive at a clear image as regards the nature of these relations. These relations were
differently political according to the circumstances of ruling, interests and the personality
of those kings.
Throughout this paper R represents commutative ring with identity, and M is a unitary left R-module. The purpose of this paper is to study a new concept, (up to our knowledge), named a semi-extending modules, as generalization of extending modules, where an Rmodule M is called semi-extending if every sub module of M is a semi-essential in a direct summand of M. Various properties of semi-extending module are considered. Moreover, we investigate the relationships between semi-extending modules and other related concepts, such as CLS-modules and FI- extending modules.
The research aims to achieve a set of objectives, the most important of which is determining the extent to which the auditors of the research sample in the Federal Bureau of Financial Supervision adhere to the requirements of the quality control system according to the Iraqi Audit Manual No. The federal financial / research sample with the quality control system according to the Iraqi audit guide No. 7), and the researcher seeks to test the main research hypothesis and sub-hypotheses, and to achieve this, a questionnaire was designed by (Google Form) and distributed electronically to the elements of the research sample, Through the statistical package program (SPSS), the results of the questionnaire were analysed. In light of the applied
... Show MoreIn this paper, we introduce and study the concept of S-coprime submodules, where a proper submodule N of an R-module M is called S-coprime submodule if M N is S-coprime Rmodule. Many properties about this concept are investigated.
Abstract Throughout this paper R represents commutative ring with identity and M is a unitary left R-module, the purpose of this paper is to study a new concept, (up to our knowledge), named St-closed submodules. It is stronger than the concept of closed submodules, where a submodule N of an R-module M is called St-closed (briefly N ≤Stc M) in M, if it has no proper semi-essential extensions in M, i.e if there exists a submodule K of M such that N is a semi-essential submodule of K then N = K. An ideal I of R is called St-closed if I is an St-closed R-submodule. Various properties of St-closed submodules are considered.
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Let R be a commutative ring with unity and let M be a unitary R-module. Let N be a proper submodule of M, N is called a coprime submodule if ï ïŽ is a coprime R-module, where ï ïŽ is a coprime R-module if for any r  R, either O  ï ïŽ ï ïŽ r or  ï ïŽ ï ïŽr . In this paper we study coprime submodules and give many properties related with this concept.
In this paper we give many connections between essentially quasi-Dedekind (quasi-
Dedekind) modules and other modules such that Baer modules, retractable modules,
essentially retractable modules, compressible modules and essentially compressible
modules where an R-module M is called essentially quasi-Dedekind (resp. quasi-
Dedekind) if, Hom(M N ,M ) 0 for all N ≤e M (resp. N ≤ M). Equivalently, a
module M is essentially quasi-Dedekind (resp. quasi-Dedekind) if, for each
f End (M) R , Kerf ≤ e M implies f = 0 (resp. f 0 implies ker f 0 ).
Let R be a commutative ring with identity and E be a unitary left R – module .We introduce and study the concept Weak Pseudo – 2 – Absorbing submodules as generalization of weakle – 2 – Absorbing submodules , where a proper submodule A of an R – module E is called Weak Pseudo – 2 – Absorbing if 0 ≠rsx A for r, s R , x E , implies that rx A + soc ( E ) or sx A + soc (E) or rs [ A + soc ( E ) E ]. Many basic properties, char
... Show More
Let R be a commutative ring with unity and let M be an R-module. In this paper we
study strongly (completely) hollow submodules and quasi-hollow submodules. We investigate
the basic properties of these submodules and the relationships between them. Also we study
the be behavior of these submodules under certain class of modules such as compultiplication,
distributive, multiplication and scalar modules. In part II we shall continue the study of these
submodules.