Prime rings

Xem 1-13 trên 13 kết quả Prime rings
  • In this paper, we present some results concerning two generalized derivations on a semiprime ring. These results are a generalization of results of M. Bresar and J. Vukman, which are related to a theorem of E. Posner for the product of derivations on a prime ring.

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  • A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. In this paper we extend Posner’s result to generalized derivations centralizing on Jordan ideals of rings with involution and discuss the related results. Moreover, we provide examples to show that the assumed restriction cannot be relaxed.

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  • In this paper, we introduce a D-H key distribution protocol over polynomial rings. These protocols use some polynomials with two cyclomic cosets in the center of the ring as part of the private keys. We give some examples over the polynomial rings Zp, where p is a prime number. We also give a security analysis of the proposed protocols and conclude that the only possible attack is by brute force.

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  • Let G be a multiplicative group. Let R be a G-graded commutative ring and M a G-graded R-module. Various properties of graded prime submodules and graded primary submodules of M are discussed. We have also discussed the graded radical of graded submodules of multiplication graded R-modules.

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  • We define and study the extended centroid of a prime semiring. We show that the extended centroid is a semifield and give some properties of the centroid of a right multiplicatively cancellable prime semiring.

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  • In this paper, we define coprimely structured rings, which are the generalization of strongly 0-dimensional rings. Furthermore, we investigate coprimely structured rings and give some relations between other rings such as Artinian rings, strongly 0 dimensional rings, and h-local domains.

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  • Here we study the graded weakly prime ideals of a G-graded commutative ring. A number of results concerning graded weakly prime ideals are given. For example, we give some characterizations of graded weakly prime ideals and their homogeneous components.

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  • The aim of this article is to discuss the existence of certain kinds of derivations and -derivations that are of period 2. Moreover, we obtain the form of generalized reverse derivations and generalized left derivations of period 2.

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  • In this paper, the authors prove that every representable module over a commutative ring with identity satisfies the radical formula. With this result, they extend the class of modules satisfying the radical formula from that of Artinian modules to a larger one. They conclude their work by giving a description of the radical of a submodule of a representable module.

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  • We classify the unmixed ideals of Veronese bi-type and in some cases we give a description of their associated prime ideals. In this paper some properties of these class of monomial ideals are discussed. In particular, our aim is to classify the unmixed Veronese bi-type ideals.

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  • We investigate the relations between a radical submodule N of a module M being a finite intersection of prime submodules of M and the factor module M/N having finite uniform dimension. It is proved that if N is a radical submodule of a module M over a ring R such that M/N has finite uniform dimension, then N is a finite intersection of prime submodules.

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  • Uniqueness properties of coprimary decompositions of modules over non-commutative rings are presented. In this paper, by making use of the technique employed, we shall prove uniqueness properties of coprimary decompositions.

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  • In this paper, we study some of the properties of gr-multiplication ideals in a graded ring R. We first characterize finitely generated gr-multiplication ideals and then give a characterization of gr-multiplication ideals by using the gr-localization of R. Finally we determine the set of gr-P primary ideals of R when P is a gr-multiplication gr-prime ideal of R.

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