منابع مشابه
F-Rationality of Determinantal Rings and Their Rees Rings
Let X be an m × n matrix (m ≤ n) of indeterminates over a field K of positive characteristic, and denote the ideal generated by its t-minors by It . We show that the Rees ringR(It ) ofK[X], as well as the algebra At generated by the t-minors, are F-rational if charK > min(t, m − t). Without a restriction on characteristic this holds for K[X]/Ir+1 and the symbolic Rees ring R(It ). The determina...
متن کاملMulti-symbolic Rees algebras and strong F-regularity
Let I be a divisorial ideal of a strongly F-regular ring A. K.-i.Watanabe raised thequestionwhether the symbolicRees algebraRs(I) = ⊕n≥0I is Cohen-Macaulay whenever it is Noetherian. We develop the notion ofmulti-symbolic Rees algebras and use this to show thatRs(I) is indeedCohen-Macaulaywhenever a certain auxiliary ring is finitely generated over A.
متن کاملRees Algebras of Modules
We study Rees algebras of modules within a fairly general framework. We introduce an approach through the notion of Bourbaki ideals that allow the use of deformation theory. One can talk about the (essentially unique) Bourbaki ideal I(E) of a module E which, in many situations, allows to reduce the nature of the Rees algebra of E to that of its Bourbaki ideal I(E). Properties such as Cohen–Maca...
متن کاملCanonical modules of Rees algebras
We compute the canonical class of certain Rees algebras. Our formula generalizes that of Herzog and Vasconcelos. Its proof relies on the fact that the formation of the canonical module commutes with subintersections in important cases. As an application we treat the classical determinantal ideals and the corresponding algebras of minors. A considerable part of Wolmer Vasconcelos’ work has been ...
متن کاملRees 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...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2002
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8998