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Keywords:
linear algebra; free module; symplectic form; symplectic basis; bilinear form
linear algebra; free module; symplectic form; symplectic basis; bilinear form
Summary:
In this paper the problem of construction of the canonical matrix belonging to symplectic forms on a module over the so called plural algebra (introduced in [5]) is solved.
References:
[1] F. W. Anderson F. K. Fuller: Rings and Categories of Modules. Springer-Verlag, New-York, 1973. MR 1245487
[2] E. Artin: Geometric Algebra. Nauka, Moskva, 1969. (In Russian.) MR 0242847 | Zbl 0174.29401
[3] M. F. Atiyah I. G. MacDonald: Introduction to Commutative Algebra. Mir, Moskva, 1972. (In Russian.) MR 0349645
[4] M. Jukl: Grassmann formula for certain type of modules. Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 3Jt (1995), 69-74. MR 1447256 | Zbl 0860.13006
[5] M. Jukl: Inertial laws of quadratic forms on modules over plural algebra. Math. Bohem. 120 (1995), 255-263. MR 1369684
[6] M. Jukl: Linear forms on free modules over certain local ring. Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 32 (1993), 49-62. MR 1273169 | Zbl 0810.13006
[7] B. R. McDonald: Geometric Algebra over Local Rings. Pure and applied mathematics. New York, 1976. MR 0476639 | Zbl 0346.20027
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