منابع مشابه
Good Ideals in Gorenstein Local Rings
Let I be an m-primary ideal in a Gorenstein local ring (A,m) with dimA = d, and assume that I contains a parameter ideal Q in A as a reduction. We say that I is a good ideal in A if G = ∑ n≥0 I n/In+1 is a Gorenstein ring with a(G) = 1−d. The associated graded ring G of I is a Gorenstein ring with a(G) = −d if and only if I = Q. Hence good ideals in our sense are good ones next to the parameter...
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Let K be a field and X an m×n matrix of indeterminates over K. Let K[X] denote the polynomial ring generated by all the indeterminates Xij . For a given positive integer r ≤ min{m, n}, we consider the determinantal ideal Ir+1 = Ir+1(X) generated by all r + 1 minors of X if r < min{m, n} and Ir+1 = (0) otherwise. Let Rr+1 = Rr+1(X) be the determinantal ring K[X]/Ir+1. Determinantal ideals and ri...
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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 Gn be the complete graph on the vertex set [n] = {1, 2, . . . , n} and ω an orientation of Gn , i.e., ω is an assignment of a direction i → j of each edge {i, j} of Gn . Let eq denote the qth unit coordinate vector of Rn . Write P(Gn ;ω) ⊂ R n for the convex hull of the (n 2 ) points ei − e j , where i → j is the direction of the edge {i, j} in the orientation ω. It will be proved that, for...
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In this paper, various elementary properties of vague rings are obtained. Furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2015
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/12970