On the theory of graded structures
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.
scientific article; zbMATH DE number 3985379
scientific article