Abstract
Buchberger’s algorithm was already studied over many kinds of rings such as principal ideal rings, noetherian valuation rings with zero divisors, Dedekind rings with zero divisors, Gaussian rings, ... . In this paper, we propose the Buchberger’s algorithm over V[e] satisfying to e 2 = 0 where V is any noetherian valuation domain and we give some applications in Zp [e] where p is a prime number and Zp = { a | a ∈ Z ,b / ∈ pZ}.
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