Ideal Bases and Valuation Rings
نویسنده
چکیده
Classical Buchberger theory is generalized to a new family of rings. The family includes all subalgebras of the polynomial algebra in one variable. Some subalgebras of polynomial algebras in several variables are included. The new rings are integral domains and have a number of other properties in common with polynomial rings. The rings sit in a field F in appropriate position relative to a valuation ring in F . The valuation ring gives rise to a totally ordered monoid which plays the role of a term ordering in the classical Buchberger theory. The paper is reasonably self-contained and contains an infinite number of examples.
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