Let R be a commutative ring with 1 and M be a (left) unitary R – module. This essay gives generalizations for the notions prime module and some concepts related to it. We termed an R – module M as semi-essentially prime if annR (M) = annR (N) for every non-zero semi-essential submodules N of M. Given some of their advantages characterizations and examples, and we study the relation between these and some classes of modules.
The definition of semi-preopen sets were first introduced by "Andrijevic" as were is defined by :Let (X , ï´ ) be a topological space, and let A ⊆, then Ais called semi-preopen set if ⊆∘ . In this paper, we study the properties of semi-preopen sets but by another definition which is equivalent to the first definition and we also study the relationships among it and (open, α-open, preopen and semi-p-open )sets.
Dans la langue française, une forme d'auxiliarité, composée de deux éléments cohérents l'auxiliant et l'auxilié, fournit, en effet, à la phrase une diversité significative et structurale. L'auxiliarité, renvoie à l'unification de deux éléments grammaticaux afin de localiser l'énoncé sur l'axe du temps, d'aspect ou de mode. É. Benveniste définit l'auxiliarité en : « Il s'agit d'une forme linguistique unitaire qui se réalise, à travers des paradigmes entiers, en deux éléments, dont chacun assume une partie des fonctions grammaticales, et qui sont à la fois liés et autonomes, distincts et complémentaires »[1]. Ces deux éléments d'auxiliarité possèden
... Show MoreThe definition of semi-preopen sets were first introduced by "Andrijevic" as were is defined by :Let (X , ï´ ) be a topological space, and let A ⊆, then A is called semi-preopen set if ⊆∘ . In this paper, we study the properties of semi-preopen sets but by another definition which is equivalent to the first definition and we also study the relationships among it and (open, α-open, preopen and semi-p-open )sets.
The main purpose of this paper is to define generalized Γ-n-derivation, study and investigate some results of generalized Γ-n-derivation on prime Γ-near-ring G and
In this paper, we investigate prime near – rings with two sided α-n-derivations
satisfying certain differential identities. Consequently, some well-known results
have been generalized. Moreover, an example proving the necessity of the primness
hypothesis is given.
In this paper, the concept of Jordan triple higher -homomorphisms on prime
rings is introduced. A result of Herstein is extended on this concept from the ring into the prime ring . We prove that every Jordan triple higher -homomorphism of ring into prime ring is either triple higher -homomorphism or triple higher -anti-homomorphism of into .
This paper investigates the concept (α, β) derivation on semiring and extend a few results of this map on prime semiring. We establish the commutativity of prime semiring and investigate when (α, β) derivation becomes zero.
This paper investigates the concept (α, β) derivation on semiring and extend a few results of this map on prime semiring. We establish the commutativity of prime semiring and investigate when (α, β) derivation becomes zero.
New types of modules named Fully Small Dual Stable Modules and Principally Small Dual Stable are studied and investigated. Both concepts are generalizations of Fully Dual Stable Modules and Principally Dual Stable Modules respectively. Our new concepts coincide when the module is Small Quasi-Projective, and by considering other kind of conditions. Characterizations and relations of these concepts and the concept of Small Duo Modules are investigated, where every fully small dual stable R-module M is small duo and the same for principally small dual stable.