منابع مشابه
A 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...
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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 کاملOn Commutative Reduced Baer Rings
It is shown that a commutative reduced ring R is a Baer ring if and only if it is a CS-ring; if and only if every dense subset of Spec (R) containing Max (R) is an extremally disconnected space; if and only if every non-zero ideal of R is essential in a principal ideal generated by an idempotent.
متن کاملDimension Sequences for Commutative Rings
Let JR be a commutative ring with identity of finite (Krull) dimension n0, and for each positive integer /c, let nk be the dimension of the polynomial ring R = R[XU . . . , Xk] in k indeterminates over R. The sequence {wjiio * Ud the dimension sequence for R, and the sequence {di}fLl9 where dt = nt — ni_1 for each i, is called the difference sequence for R. We are concerned with a determination...
متن کاملANNIHILATING SUBMODULE GRAPHS FOR MODULES OVER COMMUTATIVE RINGS
In this article, we give several generalizations of the concept of annihilating ideal graph over a commutative ring with identity to modules. Weobserve that over a commutative ring $R$, $Bbb{AG}_*(_RM)$ isconnected and diam$Bbb{AG}_*(_RM)leq 3$. Moreover, if $Bbb{AG}_*(_RM)$ contains a cycle, then $mbox{gr}Bbb{AG}_*(_RM)leq 4$. Also for an $R$-module $M$ with$Bbb{A}_*(M)neq S(M)setminus {0}$, $...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1994
ISSN: 0097-3165
DOI: 10.1016/0097-3165(94)90051-5