Let A be a noetherian ring which is locally Macaulay. For each integer i ^ O , groups d(A) and Wi(A) are denned, each sequence of groups generalizing to higher dimensions the usual class group of an integrally closed noetherian domain. d(A) is called the ith class group of A, and Wi(A) is called the ith homologuai class group of A. The main purpose of this note is to show that both sequences of...

In an earlier work the authors described a mechanism for lifting monomial ideals to reduced unions of linear varieties. When the monomial ideal is Cohen-Macaulay (including Artinian), the corresponding union of linear varieties is arithmetically CohenMacaulay. The first main result of this paper is that if the monomial ideal is Artinian then the corresponding union is in the Gorenstein linkage ...

We construct a new efficient algorithm for finding Gröbner–Shirshov bases for noncommutative algebras and their representations. This algorithm uses the Macaulay matrix [F.S. Macaulay, On some formula in elimination, Proc. London Math. Soc. 33 (1) (1902) 3–27], and can be viewed as a representation theoretic analogue of the F4 algorithm developed by J.C. Faugère. We work out some examples of un...

In this paper, we introduce the notion of “extension” of a toric variety and study its fundamental properties. This gives rise to infinitely many toric varieties with a special property, such as being set theoretic complete intersection or arithmetically Cohen-Macaulay (Gorenstein) and having a Cohen-Macaulay tangent cone or a local ring with non-decreasing Hilbert function, from just one singl...

This research began as an effort to determine exactly which one-dimensional local rings have indecomposable finitely generated modules of arbitrarily large constant rank. The approach, which uses a new construction of indecomposable modules via the bimodule structure on certain Ext groups, turned out to be effective mainly for hypersurface singularities. The argument was eventually replaced by ...

This paper examines the Macaulay, Hicks, and continuous time formulations of duration by analyzing the term structure dynamics that are necessary to derive these mathematical models. The results presented help to explain the true effects of interest rate risk upon the values of fixed-income securities, as well as provide a rationale for the development of duration models in a general equilibriu...

The main theorem says that any module-finite (but not necessarily commutative) algebra Λ over a commutative Noetherian universally catenary ring R is catenary. Hence the ring Λ is catenary if R is Cohen-Macaulay. When R is local and Λ is a Cohen-Macaulay R-module, we have that Λ is a catenary ring, dim Λ = dimΛ/Q + htΛQ for any Q ∈ Spec Λ, and the equality n = htΛQ− htΛP holds true for any pair...