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On the theory of graded structures. (English) Zbl 0609.13007
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.

MSC:
13C05 Structure, classification theorems for modules and ideals in commutative rings
18C10 Theories (e.g., algebraic theories), structure, and semantics
16W50 Graded rings and modules (associative rings and algebras)
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
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