Linear forms on free modules over certain local ring. (English) Zbl 0810.13006

Linear forms \(\varphi : M \to A\) on a free module \(M\) over the algebra \(A = \mathbb{R} [x]/x^ m\) are studied. In particular, it is proved that \(\text{Ker} \varphi\) is a hyperplane of \(M\) if and only if it exists \(y \in M\) such that \(\varphi (y) \notin \eta A\), where \(\eta\) is the element of \(A\) corresponding to \(x\).


13C10 Projective and free modules and ideals in commutative rings
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
15A63 Quadratic and bilinear forms, inner products
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[1] Atiyah M.F., MacDonald I.G.: Introducion to commutative algebra. (Russian), Mir, Moscow, 1972.
[2] McDonald B.R.: Geometric algebra over local rings. Pure and applied mathematics, New York, 1976. · Zbl 0346.20027
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