Almost Gorenstein Rees Algebras of pg-Ideals, Good Ideals, and Powers of the Maximal Ideals
نویسندگان
چکیده
منابع مشابه
Rees Algebras of Diagonal Ideals
There is a natural epimorphism from the symmetric algebra to the Rees algebra of an ideal. When this epimorphism is an isomorphism, we say that the ideal is of linear type. Given two determinantal rings over a field, we consider the diagonal ideal, kernel of the multiplication map. We prove in many cases that the diagonal ideal is of linear type and recover the defining ideal of the Rees algebr...
متن کاملGorenstein Algebras, Symmetric Matrices, Self-linked Ideals, and Symbolic Powers
Inspired by recent work in the theory of central projections onto hypersurfaces, we characterize self-linked perfect ideals of grade 2 as those with a Hilbert–Burch matrix that has a maximal symmetric subblock. We also prove that every Gorenstein perfect algebra of grade 1 can be presented, as a module, by a symmetric matrix. Both results are derived from the same elementary lemma about symmetr...
متن کاملMAXIMAL DIVISORIAL IDEALS AND t-MAXIMAL IDEALS
We give conditions for a maximal divisorial ideal to be t-maximal and show with examples that, even in a completely integrally closed domain, maximal divisorial ideals need not be t-maximal.
متن کاملGood 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...
متن کاملPowers of Ideals: Primary Decompositions, Artin-Rees Lemma and Regularity
The regularity part follows from the primary decompositions part, so the heart of this paper is the analysis of the primary decompositions. In [S], this was proved for the primary components of height at most one over the ideal. This paper proves the existence of such a k but does not provide a formula for it. In the paper [SS], Karen E. Smith and myself find explicit k for ordinary and Frobeni...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 2018
ISSN: 0026-2285
DOI: 10.1307/mmj/1516330972