Abstract
In this article, we present the theory of standard bases for modules over polynomial subalgebras based on arbitrary gradings (induced by an additive monoid Γ) which we called SΓ-bases. This paper deals with the problem of construction of SΓ-bases for submodules of free module over polynomial subalgebras. For this purpose, we present an algorithm based on SΓ-normal form and discuss it for some special gradings.
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