In this paper, we introduce the concept of s.p-semisimple module. Let S be a semiradical property, we say that a module M is s.p - semisimple if for every submodule N of M, there exists a direct summand K of M such that K ≤ N and N / K has S. we prove that a module M is s.p - semisimple module if and only if for every submodule A of M, there exists a direct summand B of M such that A = B + C and C has S. Also, we prove that for a module M is s.p - semisimple if and only if for every submodule A of M, there exists an idempotent e ∊ End(M) such that e(M) ≤ A and (1- e)(A) has S.
Let be a right module over an arbitrary ring with identity and . In this work, the coclosed rickart modules as a generalization of rickart modules is given. We say a module over coclosed rickart if for each , is a coclosed submodule of . Basic results over this paper are introduced and connections between these modules and otherwise notions are investigated.
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.
Throughout this paper we introduce the notion of coextending module as a dual of the class of extending modules. Various properties of this class of modules are given, and some relationships between these modules and other related modules are introduced.
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.
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.
Suppose that A be an abelain ring with identity, B be a unitary (left) A-module, in this paper ,we introduce a type of modules ,namely Quasi-semiprime A-module, whenever is a Prime Ideal For proper submodule N of B,then B is called Quasi-semiprime module ,which is a Generalization of Quasi-Prime A-module,whenever annAN is a prime ideal for proper submodule N of B,then B is Quasi-prime module .A comprchensive study of these modules is given,and we study the Relationship between quasi-semiprime module and quasi-prime .We put the codition coprime over cosemiprime ring for the two cocept quasi-prime module and quasi-semiprime module are equavelant.and the cocept of prime module and quasi
... Show MoreA non-zero module M is called hollow, if every proper submodule of M is small. In this work we introduce a generalization of this type of modules; we call it prime hollow modules. Some main properties of this kind of modules are investigated and the relation between these modules with hollow modules and some other modules are studied, such as semihollow, amply supplemented and lifting 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.
Let R be a ring with identity and M be a right unitary R-module. In this paper we
introduce the notion of strongly coretractable modules. Some basic properties of this
class of modules are investigated and some relationships between these modules and
other related concepts are introduced.
A field experiment was conducted at the field of the Dept. of Field Crop Sci. / College of Agriculture / University of Baghdad . The objective was to determine the values of relative constant of three – way and double crosses of maize . Ten inbreds were used and crossed during spring and fall seasons of 2009 to produce three - way and double crosses , and ten hybrids were taken from each group . The ten hybrids were grown and selfed during spring 2010 to produce 2 seed . Three way and double crosses were sown with their parents and 2 seed during fall 2010 in RCBD with four replicates . Leaf area , total dry matter , row/ear , grain/ear , grain weight and grain weight/plant of hybrids , parents and 2 plants were taken . Results showed that
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