S-Sequences and Monomial Modules

Gioia Failla,Paola Lea Staglianó

doi:10.3390/math9212659

Abstract

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 Noetherian ring with unit, has a specific initial module with respect to an admissible order, provided M is generated by an s-sequence. Significant examples complement the results.

Highlights

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Since the main idea in the use of Gröbner bases is to reduce all problems to questions of monomial ideals, we study the monomial submodules ⊕ Ii ei, where all Ii are monomial ideals
The aim of this paper is to investigate the symmetric algebra of a monomial module M = ⊕ Ii ei, a submodule of Rn, R = K [ x1, . . . , xm ], K a field, and I1, . . . , In monomial ideals of R, via the theory of s-sequences [8,9,10]. the In Section 2, we review basic concepts of the theory of s-sequences and results about the main algebraic and homological invariants of the symmetric algebra of a finitely generated graded R-module M, generated by an s-sequence, provided R is a standard graded K-algebra and the generators of M

Summary

Introduction

< en , we formulate sufficient conditions to be a monomial module M generated by an s-sequence. We give an application to the first syzygy module of the class of mixed product ideals in two sets of variables [11,12], generated by an s-sequence [13,14,15]. Let M be a graded R-module, R a standard graded algebra, generated by a homogeneous s-sequence f 1 , .

Objectives

Results

Conclusion