منابع مشابه
Duality Theorems for Crossed Products over Rings
In this note we extend duality theorems for crossed products obtained by M. Koppinen and C. Chen from the case of a base field or a Dedekind domain to the case of an arbitrary noetherian commutative ground ring under fairly weak conditions. In particular we extend an improved version of the celebrated Blattner-Montgomery duality theorem to the case of arbitrary noetherian ground rings.
متن کاملOrthogonal Groups over Local Rings
In an earlier paper [S] we have determined the structure of the linear groups over a local ring. In this note we continue the study of the classical groups over a local ring with the investigation of the orthogonal groups. Our main result (cf. Theorem 6 below) is a complete description of the invariant subgroups of an orthogonal group of noncompact type (i.e., of index ^ 1) over a local ring L ...
متن کاملBounds in Polynomial Rings over Artinian Local Rings
Let R be a (mixed characteristic) Artinian local ring of length l and let X be an n-tuple of variables. This paper provides bounds over the ring R[X] on the degrees of the output of several algebraic constructions in terms of l, n and the degrees of the input. For instance, if I is an ideal in R[X] generated by polynomials gi of degree at most d and if f is a polynomial of degree at most d belo...
متن کاملDuality Preserving Gray Maps for Codes over Rings
Given a finite ring A which is a free left module over a subring R of A, two types of R-bases, pseudo-self-dual bases (similar to trace orthogonal bases) and symmetric bases, are defined which in turn are used to define duality preserving maps from codes over A to codes over R. Both types of bases are generalizations of similar concepts for fields. Many illustrative examples are given to shed l...
متن کاملPeriodic modules over Gorenstein local rings
It is proved that the minimal free resolution of a module M over a Gorenstein local ring R is eventually periodic if, and only if, the class of M is torsion in a certain Z[t ±1 ]-module associated to R. This module, denoted J(R), is the free Z[t ±1 ]-module on the isomorphism classes of finitely generated R-modules modulo relations reminiscent of those defining the Grothendieck group of R. The ...
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ژورنال
عنوان ژورنال: Topology
سال: 1962
ISSN: 0040-9383
DOI: 10.1016/0040-9383(62)90104-0