On the theory of graded structures
type: Item
instance of: scholarly article
title: On the theory of graded structures
zbMATH Open document ID: 0609.13007
DOI: 10.1016/S0747-7171(86)80019-0
author: Lorenzo Robbiano
published in: Journal of Symbolic Computation
publication date: 1986-01-01T00:00:00Z
review text: A new structural algebraic framework is given to the concept and the construction of the generalized standard bases. Graded structure over a commutative ring \(A\), \(v\)-filtered structure on \(A\), modules over a graded structure, modules on the \(v\)-filtered structures and the corresponding morphisms as well as their relationship are considered from the categorical point of view. Finite modules over a noetherian structure in connection with Krull modules are discussed. Attention is paid to generalized standard bases of a module, noetherian graded structures, finite Krull modules, special morphisms, free resolutions and double structures on \(A\). The exposition would look better if a reference to category theory was applied, definitions 5, 9 need to be more precise and complete as well as the corresponding statements. Some of the author's results are not enough distinguished from known statements.
Mathematics Subject Classification ID: 13C05
Mathematics Subject Classification ID: 18C10
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 13F20
zbMATH DE Number: 3985379
zbMATH Keywords: Gröbner bases
zbMATH Keywords: generalized standard bases
zbMATH Keywords: noetherian graded structures
zbMATH Keywords: finite Krull modules
reviewed by: Ketty Peeva
MaRDI profile type: Publication
cites work: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal
cites work: Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems
cites work: Q3714165
cites work: Q4050885
cites work: Finite Generation of Noetherian Graded Rings
cites work: Resolution of singularities of an algebraic variety over a field of characteristic zero. I
cites work: Q3685189
cites work: Q3708893
cites work: On the equations defining tangent cones
cites work: Q3222965
cites work: Form rings and regular sequences
description: scientific article; zbMATH DE number 3985379