منابع مشابه
Prime Lie Rings of Generalized Derivations of Commutative Rings
Let R be a commutative ring with identity. By a Bres̃ar generalized derivation of R we mean an additive map g : R→ R such that g (xy) = g (x) y + xd (y) for all x, y ∈ R, where d is a derivation of R. And an additive mapping f : R → R is called a generalized derivation in the sense of Nakajima if it satisfies f(xy) = f(x)y + xf(y) − xf(1)y for all x, y ∈ R. In this paper we extend some results o...
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In [2] Singer and Wermer showed that a bounded derivation in a commutative Banach algebra 21 necessarily maps 21 into the radical 91. They conjectured at this time that the assumption of boundedness could be dropped. It is a corollary of results proved below that if 21 is in addition regular and semi-simple, this is indeed the case. What is actually proved here is that under the above hypothese...
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...
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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 کاملSimple derivations of differentiably simple Noetherian commutative rings in prime characteristic
Let R be a differentiably simple Noetherian commutative ring of characteristic p > 0 (then (R,m) is local with n := emdim(R) < ∞). A short proof is given of the Theorem of Harper [1] on classification of differentiably simple Noetherian commutative rings in prime characteristic. The main result of the paper is that there exists a nilpotent simple derivation of the ring R such that if δ i 6= 0 t...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1984
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-48-1-7-16