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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 \(x\).

MSC:

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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References:

[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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