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quadratic forms over a real plural algebra; plural signature; inertia theorem; free module; bilinear form; polar basis; linear algebra; quadratic form
Quadratic forms on a free finite-dimensional module are investigated. It is shown that the inertial law can be suitably generalized provided the vector space is replaced by a free finite-dimensional module over a certain linear algebra over $\R$ ( real plural algebra) introduced in [1].
[1] M. Jukl: Linear forms on free modules over certain local ring. Acta UP Olomouc, Fac. rer. nat. 110; Matematica 32 (1993), 49-62. MR 1273169 | Zbl 0810.13006
[2] M. F. Atiyah, I. G. MacDonald: Introduction to commutative algebra. Addison-Wesley, Reading, Massachusetts, 1969. MR 0242802 | Zbl 0175.03601
[3] B. R. McDonald: Geometric algebra over local rings. Pure and applied mathematics. New York, 1976. MR 0476639 | Zbl 0346.20027
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