Cyclic purity versus purity in excellent Noetherian rings
نویسندگان
چکیده
منابع مشابه
Purity and Gorenstein Filtered Rings
In this paper, we discuss on the existence of filtrations of modules having good properties. In particular, we focus on filtered homomorphisms called strict, and show that there exists a filtration which makes a filtered homomorphism a strict filtered homomorphism. Moreover, by using this result, we study purity for filtered modules over a Gorenstein filtered ring.
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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...
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ly considered from such construction; and which doth accompany it though otherwise constructed than is supposed.7 Wallis thus saw geometrical knowledge as more concerned with construction-invariant features of geometrical figures than with features deriving from their construction. In addition, he saw algebraic 5. Idem, p. 230 6. Knowing via minimal or simplest cause would have been better stil...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1977
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1977-0463152-5