Department of Correspondence Studies, Panjab University, Chandigarh - 160 014
A theory of anti-hermitian form over a commutative ring with identity having an involution is being proposed. The work is based on the observations of E. Witt who observed equivalence classes of anisotropic quadratic forms may be viewed as the quotient ring of the integral group ring Z[G] by an ideal Á, where G @ F*/ (F*)2 and Á is the ideal generated by elements of the form (g1 + g2 - g3 - g4) and (1+g5) with gi ÎG. The results hold for l- hermitian forms where l is such that l.l* = 1.
Key words: Antihermitian form, idempotent, involution, witt-ring.