On Semiprime Goldie Modules
نویسندگان
چکیده
منابع مشابه
On Semiprime Right Goldie Mccoy Rings
In this note we first show that for a right (resp. left) Ore ring R and an automorphism σ of R, if R is σ-skew McCoy then the classical right (resp. left) quotient ring Q(R) of R is σ̄-skew McCoy. This gives a positive answer to the question posed in Başer et al. [1]. We also characterize semiprime right Goldie (von Neumann regular) McCoy (σ-skew McCoy) rings.
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Let R be a ring, σ an injective endomorphism of R and δ a σderivation of R. We prove that if R is semiprime left Goldie then the same holds for the Ore extension R[x;σ, δ] and both rings have the same left uniform dimension.
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We find a bound for the Goldie dimension of hereditary modules in terms of the cardinality of the generator sets of its quasi-injective hull. Several consequences are deduced. In particular, it is shown that every right hereditary module with countably generated quasi-injective hull is noetherian. Or that every right hereditary ring with finitely generated injective hull is artinian, thus answe...
متن کاملCentralizers on semiprime rings
The main result: Let R be a 2-torsion free semiprime ring and let T : R → R be an additive mapping. Suppose that T (xyx) = xT (y)x holds for all x, y ∈ R. In this case T is a centralizer.
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2016
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2015.1113290