The main objective of this thesis is to study new concepts (up to our knowledge) which are P-rational submodules, P-polyform and fully polyform modules. We studied a special type of rational submodule, called the P-rational submodule. A submodule N of an R-module M is called P-rational (Simply, N≤_prM), if N is pure and Hom_R (M/N,E(M))=0 where E(M) is the injective hull of M. Many properties of the P-rational submodules were investigated, and various characteristics were given and discussed that are analogous to the results which are known in the concept of the rational submodule. We used a P-rational submodule to define a P-polyform module which is contained properly in the polyform module. An R-module M is called P-polyform if every essential submodule of M is P-rational in M. We study this kind of module in some detail and introduced some characterizations of the P-polyform module and its relationships with some other modules. The third kind of module in this thesis is called fully polyform module, and it is contained in the class of polyform module. A module M is said to be fully polyform, if every P-essential submodule of M is rational in M, that is Hom_R(M/N, E(M))=0 for every P-essential submodule N of M. In fact, the class of fully polyform modules lies between polyform modules and essentially quasi-Dedekind modules. The main characteristics of fully polyform modules were investigated, and some characterizations of these types of modules were established. Furthermore, the relationships between this class and other related modules were examined.
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In this paper, we introduce and study a new concept (up to our knowledge) named CL-duo modules, which is bigger than that of duo modules, and smaller than weak duo module which is given by Ozcan and Harmanci. Several properties are investigated. Also we consider some characterizations of CL-duo modules. Moreover, many relationships are given for this class of modules with other related classes of modules such as weak duo modules, P-duo modules.
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Let R be a commutative ring with identity, and let M be a unitary left R-module. M is called Z-regular if every cyclic submodule (equivalently every finitely generated) is projective and direct summand. And a module M is F-regular if every submodule of M is pure. In this paper we study a class of modules lies between Z-regular and F-regular module, we call these modules regular modules.
Let R be a commutative ring with identity, and let M be a unitary left R-module. M is called special selfgenerator or weak multiplication module if for each cyclic submodule Ra of M (equivalently, for each submodule N of M) there exists a family {fi} of endomorphism of M such that Ra = ∑_i▒f_i (M) (equivalently N = ∑_i▒f_i (M)). In this paper we introduce a class of modules properly contained in selfgenerator modules called special selfgenerator modules, and we study some of properties of these modules.
Throughout this paper we introduce the concept of quasi closed submodules which is weaker than the concept of closed submodules. By using this concept we define the class of fully extending modules, where an R-module M is called fully extending if every quasi closed submodule of M is a direct summand.This class of modules is stronger than the class of extending modules. Many results about this concept are given, also many relationships with other related concepts are introduced.
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The study of properties of space of entire functions of several complex variables was initiated by Kamthan [4] using the topological properties of the space. We have introduced in this paper the sub-space of space of entire functions of several complex variables which is studied by Kamthan.
Promoting the production of industrially important aromatic chloroamines over transition-metal nitrides catalysts has emerged as a prominent theme in catalysis. This contribution provides an insight into the reduction mechanism of p-chloronitrobenzene (p-CNB) to p-chloroaniline (p-CAN) over the γ-Mo2N(111) surface by means of density functional theory calculations. The adsorption energies of various molecularly adsorbed modes of p-CNB were computed. Our findings display that, p-CNB prefers to be adsorbed over two distinct adsorption sites, namely, Mo-hollow face-centered cubic (fcc) and N-hollow hexagonal close-packed (hcp) sites with adsorption energies of −32.1 and −38.5 kcal/mol, respectively. We establish that the activation of nit
... Show MoreIn this paper, we introduce the concepts of Large-lifting and Large-supplemented modules as a generalization of lifting and supplemented modules. We also give some results and properties of this new kind of modules.
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