منابع مشابه
Fixed Subrings of Noetherian Graded Regular Rings
Rings of invariants can have nice homological properties even if they do not have finite global dimension. Watanabe’s Theorem [W] gives conditions when the fixed subring of a commutative ring under the action of a finite group is a Gorenstein ring. The Gorenstein condition was extended to noncommutative rings by a condition explored by Idun Reiten in the 1970s, called k-Gorenstein in [FGR]. Thi...
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An easy consequence of this is that a left Noetherian (respectively left Artinian) ring which is finitely generated over its center is right Noetherian (respectively right Artinian). Theorem 1 follows easily from Theorem 2, which gives a partial converse to the following standard fact: IfR C S are rings, and ifQ is an injective R-module, then Hom~(S, Q) is an injective S-module (this follows, f...
متن کاملFactorial and Noetherian Subrings of Power Series Rings
Let F be a field. We show that certain subrings contained between the polynomial ring F [X] = F [X1, · · · , Xn] and the power series ring F [X][[Y ]] = F [X1, · · · , Xn][[Y ]] have Weierstrass Factorization, which allows us to deduce both unique factorization and the Noetherian property. These intermediate subrings are obtained from elements of F [X][[Y ]] by bounding their total X-degree abo...
متن کاملFully Bounded Noetherian Rings
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...
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When Sarah Glaz, Bill Heinzer and the junior author of this article approached Robert with the idea of editing a book dedicated to his work, we asked him to give us a list of his work and to comment on it to the extent he felt comfortable. As usual, he was extremely thorough in his response. When the authors of this article began to consider what topic we wanted to write about, we were impresse...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1974
ISSN: 0002-9939
DOI: 10.2307/2039890