Completions of Noetherian hereditary prime rings
نویسندگان
چکیده
منابع مشابه
Hereditary Noetherian Prime Rings
In the study of hereditary Noetherian rings, it is clear that hereditary Noetherian prime rings will play a central role (see, for example, [12]). Here we study the (two-sided) ideals of an hereditary Xoetherian prime ring and, as a consequence, ascertain the structure of factor rings and torsion modules. The torsion theory represents a generalization of similar results about Dedekind prime rin...
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We generalize two major ways of obtaining derived equivalences, the tilting process by Happel, Reiten and Smalø and Happel’s Tilting Theorem, to the setting of finitely presented modules over right coherent rings. Moreover, we extend the characterization of quasi–tilted artin algebras as the almost hereditary ones to all right noetherian rings. We also give a streamlined and general presentatio...
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We study prime ideals in skew power series rings T := R[[y; τ, δ]], for suitably conditioned complete right noetherian rings R, automorphisms τ of R, and τ -derivations δ of R. Such rings were introduced by Venjakob, motivated by issues in noncommutative Iwasawa theory. Our main results concern “Cutting Down” and “Lying Over.” In particular, assuming that τ extends to a compatible automorphsim ...
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Let i : A → R be a ring morphism, and χ : R → A a right R-linear map with χ(χ(r)s) = χ(rs) and χ(1 R) = 1 A. If R is a Frobenius A-ring, then we can define a trace map tr : A → A R. If there exists an element of trace 1 in A, then A is right FBN if and only if A R is right FBN and A is right noetherian. The result can be generalized to the case where R is an I-Frobenius A-ring. We recover resul...
متن کاملOn Nonnil-Noetherian Rings
Let R be a commutative ring with 1 such that Nil(R) is a divided prime ideal of R. The purpose of this paper is to introduce a new class of rings that is closely related to the class of Noetherian rings. A ring R is called a Nonnil-Noetherian ring if every nonnil ideal of R is finitely generated. We show that many of the properties of Noetherian rings are also true for Nonnil-Noetherian rings; ...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1980
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1980.90.285