منابع مشابه
Representation of real commutative rings
During the last 10 years there have been several results on the representation of real polynomials, positive on some semi-algebraic subset of R. These results started with a solution of the moment problem by Schmüdgen for corresponding sets. Later Wörmann realized that the same results could be obtained by the so-called “Kadison-Dubois” Representation Theorem. The aim of our talk is to present ...
متن کاملON COMMUTATIVE GELFAND RINGS
A ring is called a Gelfand ring (pm ring ) if each prime ideal is contained in a unique maximal ideal. For a Gelfand ring R with Jacobson radical zero, we show that the following are equivalent: (1) R is Artinian; (2) R is Noetherian; (3) R has a finite Goldie dimension; (4) Every maximal ideal is generated by an idempotent; (5) Max (R) is finite. We also give the following resu1ts:an ideal...
متن کاملAssociated Graphs of Modules Over Commutative Rings
Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. In this paper we introduce a new graph associated to modules over commutative rings. We study the relationship between the algebraic properties of modules and their associated graphs. A topological characterization for the completeness of the special subgraphs is presented. Also modules whose associated graph is complete...
متن کاملA General Representation Theorem for Partially Ordered Commutative Rings
An extension of the Kadison-Dubois representation theorem is proved. This extends both the classical version [3] and the preordering version given by Jacobi in [5]. It is then shown how this can be used to sharpen the results on representations of strictly positive polynomials given by Jacobi and Prestel in [6]. In [4] Dubois extends a result of Kadison on representation of archimedean partiall...
متن کاملExact annihilating-ideal graph of commutative rings
The rings considered in this article are commutative rings with identity $1neq 0$. The aim of this article is to define and study the exact annihilating-ideal graph of commutative rings. We discuss the interplay between the ring-theoretic properties of a ring and graph-theoretic properties of exact annihilating-ideal graph of the ring.
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ژورنال
عنوان ژورنال: Expositiones Mathematicae
سال: 2005
ISSN: 0723-0869
DOI: 10.1016/j.exmath.2005.01.017