منابع مشابه
ON 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...
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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 کاملNon-commutative reduction rings
Reduction relations are means to express congruences on rings. In the special case of congruences induced by ideals in commutative polynomial rings, the powerful tool of Gröbner bases can be characterized by properties of reduction relations associated with ideal bases. Hence, reduction rings can be seen as rings with reduction relations associated to subsets of the ring such that every finitel...
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 کاملCommutative Monoid Rings as Hilbert Rings
Let S be a cancellative monoid with quotient group of torsion-free rank a. We show that the monoid ring R[S] is a Hilbert ring if and only if the polynomial ring R[{ X, },s/] is a Hilbert ring, where |/| = a. Assume that R is a commutative unitary ring and G is an abelian group. The first research problem listed in [K, Chapter 7] is that of determining equivalent conditions in order that the gr...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1984
ISSN: 0022-4049
DOI: 10.1016/0022-4049(84)90011-2