In this article, we study the notion of closed Rickart modules. A right R-module M is said to be closed Rickart if, for each , is a closed submodule of M. Closed Rickart modules is a proper generalization of Rickart modules. Many properties of closed Rickart modules are investigated. Also, we provide some characterizations of closed Rickart modules. A necessary and sufficient condition is provided to ensure that this property is preserved under direct sums. Several connections between closed Rickart modules and other classes of modules are given. It is shown that every closed Rickart module is -nonsingular module. Examples which delineate this concept and some results are provided.
Let R be a commutative ring with identity, and let M be a unitary R-module. We introduce a concept of almost bounded submodules as follows: A submodule N of an R-module M is called an almost bounded submodule if there exists xÃŽM, xÃN such that annR(N)=annR(x).
In this paper, some properties of almost bounded submodules are given. Also, various basic results about almost bounded submodules are considered.
Moreover, some relations between almost bounded submodules and other types of modules are considered.
Every finite dimensional normed algebra is isomorphic to the finite direct product of or , it is also proved these algebras are ultrasemiprime algebras. In this paper, the ultrasemiprime proof of the finite direct product of and is generalized to the finite direct product of any ultrasemiprime algebras.
Let R be associative; ring; with an identity and let D be unitary left R- module; . In this work we present semiannihilator; supplement submodule as a generalization of R-a- supplement submodule, Let U and V be submodules of an R-module D if D=U+V and whenever Y≤ V and D=U+Y, then annY≪R;. We also introduce the the concept of semiannihilator -supplemented ;modules and semiannihilator weak; supplemented modules, and we give some basic properties of this conseptes.
Let R be a commutative ring with identity, and M be unital (left) R-module. In this paper we introduce and study the concept of small semiprime submodules as a generalization of semiprime submodules. We investigate some basis properties of small semiprime submodules and give some characterizations of them, especially for (finitely generated faithful) multiplication modules.
Most of the Weibull models studied in the literature were appropriate for modelling a continuous random variable which assumes the variable takes on real values over the interval [0,∞]. One of the new studies in statistics is when the variables take on discrete values. The idea was first introduced by Nakagawa and Osaki, as they introduced discrete Weibull distribution with two shape parameters q and β where 0 < q < 1 and b > 0. Weibull models for modelling discrete random variables assume only non-negative integer values. Such models are useful for modelling for example; the number of cycles to failure when components are subjected to cyclical loading. Discrete Weibull models can be obta
... Show MoreLet 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.
Let R be an associative ring with identity and let M be right R-module M is called μ-semi hollow module if every finitely generated submodule of M is μ-small submodule of M The purpose of this paper is to give some properties of μ-semi hollow module. Also, we gives conditions under, which the direct sum of μ-semi hollow modules is μ-semi hollow. An R-module is said has a projective μ-cover if there exists an epimorphism
Jordan curve theorem is one of the classical theorems of mathematics, it states the following : If is a graph of a simple closed curve in the complex plane the complement of is the union of two regions, being the common boundary of the two regions. One of the region is bounded and the other is unbounded. We introduced in this paper one of Jordan's theorem generalizations. A new type of space is discussed with some properties and new examples. This new space called Contractible -space.