Polynomial Iungs over Jacobsoñ-hilbert Rings

نویسنده

  • CARL FAITH
چکیده

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 the cace .

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

HILBERT SCHEMES and MAXIMAL BETTI NUMBERS over VERONESE RINGS

We show that Macaulay’s Theorem, Gotzmann’s Persistence Theorem, and Green’s Theorem hold over a Veronese toric ring R. We also prove that the Hilbert scheme over R is connected; this is an analogue of Hartshorne’s theorem that the Hilbert scheme over a polynomial ring is connected. Furthermore, we prove that each lex ideal in R has the greatest Betti numbers among all graded ideals with the sa...

متن کامل

Gray Images of Constacyclic Codes over some Polynomial Residue Rings

Let  be the quotient ring    where  is the finite field of size   and  is a positive integer. A Gray map  of length  over  is a special map from  to ( . The Gray map   is said to be a ( )-Gray map if the image of any -constacyclic code over    is a -constacyclic code over the field   . In this paper we investigate the existence of   ( )-Gray maps over . In this direction, we find an equivalent ...

متن کامل

On Gröbner bases and Krull dimension of residue class rings of polynomial rings over integral domains

Given an ideal a in A[x1, . . . , xn] where A is a Noetherian integral domain, we propose an approach to compute the Krull dimension of A[x1, . . . , xn]/a, when the residue class ring is a free A-module. When A is a field, the Krull dimension of A[x1, . . . , xn]/a has several equivalent algorithmic definitions by which it can be computed. But this is not true in the case of arbitrary Noetheri...

متن کامل

Chow Rings of Matroids and Atomistic Lattices

After Feichner and Yuzvinsky introduced the Chow ring associated to ranked atomistic lattices in 2003, little study of them was made before Adiprisito, Huh, and Katz used them to resolve the long-standing Heron-Rota-Walsh conjecture, proving along the way that the Chow rings of geometric lattices satisfy versions of Poincaré duality, the hard Lefschetz theorem, and the Hodge-Riemann relations. ...

متن کامل

Gl-equivariant Modules over Polynomial Rings in Infinitely Many Variables

Consider the polynomial ring in countably infinitely many variables over a field of characteristic zero, together with its natural action of the infinite general linear group G. We study the algebraic and homological properties of finitely generated modules over this ring that are equipped with a compatible G-action. We define and prove finiteness properties for analogues of Hilbert series, sys...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2006