6 Results Found

In this paper we study a monomial module M generated by an s-sequence and the main algebraic and homological invariants of the symmetric algebra of M. We show that the first syzygy module of a finitely generated module M, over any commutative Noether...

Let S be a polynomial ring in n variables over a field K of any characteristic. Given a strongly stable submodule M of a finitely generated graded free S-module F, we propose a method for constructing a standard Borel-fixed submodule $\tilde{M}$ of F...

In 1982, Stanley predicted a combinatorial upper bound for the depth of any finitely generated multigraded module over a polynomial ring. The predicted invariant is now called the Stanley depth. Duval et al. found a counterexample for Stanley’s...

H-bases provide an attractive alternative to Gröbner bases for the study of polynomial ideals because they are independent of monomial orderings and therefore preserve structural properties that may be obscured in Gröbner basis computations...

In this paper, we discuss a few simple methods for computing the local topological index and its various analogs for vector fields and differential forms given on complex varieties with singularities of different types. They are based on properties o...

Minimal free resolutions of a finitely generated module over a polynomial ring $S=k\left[\mathbf{x}\right]$, with variables $\mathbf{x}=\{x_1,\dots ,x_n\}$ and a field k have been extensively studied. Almost all the results in the literature about minimal free resolutions give their B...