Let M be an R-module, where R is a commutative ring with unity. A submodule N of M is called e-small (denoted by N e  M) if N + K = M, where K e  M implies K = M. We give many properties related with this type of submodules.
Currently, there is no established of e-waste treatment in Thi- Qar province, while their creating is increasing every year. It has been well- known that e-waste is a source of environmental degrading and their placement in landfills increases the irreversible climate change. A research model has been developed to link three components: coercive pressure, normative influence, and mimicry, then study their effect on e-waste adopt and continuance intentions. The model was validated using data collected from a field survey of 92 managers of small enterprises in Thi-Qar province. A questionnaire was developed to collect data. It contains five major variables, exemplify by fourteen items. Als
... Show MoreThroughout this paper R represents a commutative ring with identity and all R-modules M are unitary left R-modules. In this work we introduce the notion of S-maximal submodules as a generalization of the class of maximal submodules, where a proper submodule N of an R-module M is called S-maximal, if whenever W is a semi essential submodule of M with N ? W ? M, implies that W = M. Various properties of an S-maximal submodule are considered, and we investigate some relationships between S-maximal submodules and some others related concepts such as almost maximal submodules and semimaximal submodules. Also, we study the behavior of S-maximal submodules in the class of multiplication modules. Farther more we give S-Jacobson radical of ri
... Show MoreThroughout this paper R represents a commutative ring with identity and all R-modules M are unitary left R-modules. In this work we introduce the notion of S-maximal submodules as a generalization of the class of maximal submodules, where a proper submodule N of an R-module M is called S-maximal, if whenever W is a semi essential submodule of M with N ⊊ W ⊆ M, implies that W = M. Various properties of an S-maximal submodule are considered, and we investigate some relationships between S-maximal submodules and some others related concepts such as almost maximal submodules and semimaximal submodules. Also, we study the behavior of S-maximal submodules in the class of multiplication modules. Farther more we give S-Jacobson radical of rings
... Show MoreThe goal of this research is to introduce the concepts of Large-small submodule and Large-hollow module and some properties of them are considered, such that a proper submodule N of an R-module M is said to be Large-small submodule, if N + K = M where K be a submodule of M, then K is essential submodule of M ( K ≤e M ). An R-module M is called Large-hollow module if every proper submodule of M is Large-small submodule in M.
Let R be an individual left R-module of the same type as W, with W being a ring containing one. W’s submodules N and K should be referred to as N and K, respectively that K ⊆ N ⊆ W if N/K <<_J (D_j (W)+K)/K, Then K is known as the D J-coessential submodule of Nin W as K⊆_ (Rce) N. Coessential submodule is a generalization of this idea. These submodules have certain interesting qualities, such that if a certain condition is met, the homomorphic image of D J- N has a coessential submodule called D J-coessential submodule.
A non-zero submodule N of M is called essential if N L for each non-zero submodule L of M. And a non-zero submodule K of M is called semi-essential if K P for each non-zero prime submodule P of M. In this paper we investigate a class of submodules that lies between essential submodules and semi-essential submodules, we call these class of submodules weak essential submodules.
Through this paper R represent a commutative ring with identity and all R-modules are unitary left R-modules. In this work we consider a generalization of the class of essential submodules namely annihilator essential submodules. We study the relation between the submodule and his annihilator and we give some basic properties. Also we introduce the concept of annihilator uniform modules and annihilator maximal submodules.
Let be a commutative ring with 1 and be left unitary . In this paper we introduced and studied concept of semi-small compressible module (a is said to be semi-small compressible module if can be embedded in every nonzero semi-small submodule of . Equivalently, is semi-small compressible module if there exists a monomorphism , , is said to be semi-small retractable module if , for every non-zero semi-small sub module in . Equivalently, is semi-small retractable if there exists a homomorphism whenever . In this paper we introduce and study the concept of semi-small compressible and semi-small retractable s as a generalization of compressible and retractable respectively and give some of their adv
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