Security and Privacy in Three States of Information

In regard to computational context, information can be in either of three states at a time: in transit, in process, or in storage. When the security and privacy of information is of concern, each of these states should be addressed exclusively, i.e., network security, computer security, and database/cloud security, respectively. This chapter first introduces the three states of information and then addresses the security as well as privacy issues that relate to each state. It provides practical examples for each state discussed, introduces corresponding security and privacy algorithms for explaining the concepts, and facilitates their implementation whenever needed. Moreover, the security and privacy techniques pertaining to the three states of information are combined together to offer a more comprehensive and realistic consideration of everyday security practices

1-absorbing primary submodules

Let R be a commutative ring with non-zero identity and M be a unitary R-module. The goal of this paper is to extend the concept of 1-absorbing primary ideals to 1-absorbing primary submodules. A proper submodule N of M is said to be a 1-absorbing primary submodule if whenever non-unit elements a, b is an element of R and m is an element of M with abm is an element of N, then either ab is an element of (N :(R) M) or m is an element of M - rad(N). Various properties and chacterizations of this class of submodules are considered. Moreover, 1-absorbing primary avoidance theorem is proved

Probing a Nucleon Spin Structure at TESLA by the Real Polarized Gamma Beam

The recent proposals concerning the usage of the real polarized gamma beam, obtained by the Compton backscattering of the laser photons off the electron beams from either the linear or circular accelerators were considered. The heavy quark photoproduction process giving a unique opportunity to measure polarized gluon distribution was investigated.Comment: 16 pages, LATEX, 6 figures (EPS

Weakly J-ideals of Commutative Rings

Let $R$ be a commutative ring with non-zero identity. In this paper, we introduce the concept of weakly $J$-ideals as a new generalization of $J$-ideals. We call a proper ideal $I$ of a ring $R$ a weakly $J$-ideal if whenever $a,b\in R$ with $0\neq ab\in I$ and $a\notin J(R)$, then $a\in I$. Many of the basic properties and characterizations of this concept are studied. We investigate weakly $J$-ideals under various contexts of constructions such as direct products, localizations, homomorphic images. Moreover, a number of examples and results on weakly $J$-ideals are discussed. Finally, the third section is devoted to the characterizations of these constructions in an amagamated ring along an ideal

Quasi J-ideals of Commutative Rings

Let $R$ be a commutative ring with identity. In this paper, we introduce the concept of quasi $J$-ideal which is a generalization of $J$-ideal. A proper ideal of $R$ is called a quasi $J$-ideal if its radical is a $J$-ideal. Many characterizations of quasi $J$-ideals in some special rings are obtained. We characterize rings in which every proper ideal is quasi $J$-ideal. Further, as a generalization of presimplifiable rings, we define the notion of quasi presimplifiable rings. We call a ring $R$ a quasi presimplifiable ring if whenever $a,b\in R$ and $a=ab$, then either $a$ is a nilpotent or $b$ is a unit. It is shown that a proper ideal $I$ that is contained in the Jacobson radical is a quasi $J$-ideal (resp. $J$-ideal) if and only if $R/I$ is a quasi presimplifiable (resp. presimplifiable) ring

Semi r-ideals of commutative rings

For commutative rings with identity, we introduce and study the concept of semi r-ideals which is a kind of generalization of both r-ideals and semiprime ideals. A proper ideal I of a commutative ring R is called semi r-ideal if whenever a (2)?I and Ann (R)(a) = 0, then a ? I. Several properties and characterizations of this class of ideals are determined. In particular, we investigate semi r-ideal under various contexts of constructions such as direct products, localizations, homomorphic images, idealizations and amalagamations rings. We extend semi r-ideals of rings to semi r-submodules of modules and clarify some of their properties. Moreover, we define submodules satisfying the D-annihilator condition and justify when they are semi r-submodules