Which series are Hilbert series of graded modules over standard multigraded polynomial rings?
نویسندگان
چکیده
منابع مشابه
Standard bases in mixed power series and polynomial rings over rings
In this paper we study standard bases for submodules of a mixed power series and polynomial ring RJt1, . . . , tmK[x1, . . . , xn] s respectively of their localization with respect to a t-local monomial ordering for a certain class of noetherian rings R. The main steps are to prove the existence of a division with remainder generalizing and combining the division theorems of Grauert–Hironaka an...
متن کاملModules over Differential Polynomial Rings
This note announces a number of results on the structure of differential modules over differential rings, where differential ring means a ring with a family of derivations and differential module means a module having a family of operators compatible with the derivations of the ring. To fix notation, throughout the paper we let A denote an associative ring, M = AM an 4-module, k the correspondi...
متن کاملCombinatorics of Multigraded Poincaré Series for Monomial Rings
Backelin proved that the multigraded Poincaré series for resolving a residue field over a polynomial ring modulo a monomial ideal is a rational function. The numerator is simple, but until the recent work of Berglund there was no combinatorial formula for the denominator. Berglund’s formula gives the denominator in terms of ranks of reduced homology groups of lower intervals in a certain lattic...
متن کاملPolynomial Iungs over Jacobsoñ-hilbert Rings
CARL FAITH All rings considered are commutative with unit. A ring R is SISI (in Vámos' terminology) if every subdirectly irreducible factor ring R/I is self-injective . SISI rings include Noetherian rings, Morita rings, and almost maximal valuation rings ([Vil) . In [F3] we raised the question of whether a polynomial ring R[-1 over a SISI ring R is again SISI . In this paper we show this is not...
متن کاملStable polynomial division and essential normality of graded Hilbert modules
The purpose of this paper is to initiate a new attack on Arveson’s resistant conjecture, that all graded submodules of the d-shift Hilbert module H are essentially normal. We introduce the stable division property for modules (and ideals): a normed module M over the ring of polynomials in d variables has the stable division property if it has a generating set {f1, . . . , fk} such that every h ...
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: Mathematische Nachrichten
سال: 2019
ISSN: 0025-584X,1522-2616
DOI: 10.1002/mana.201800436