Geodesic
Generators of Un(V) Over a Quasi Semilocal Semihereditary Ring
Canadian journal of mathematics, Tome 33 (1981) no. 5, pp. 1232-1244

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Let o be a quasi semilocal semihereditary ring, i.e., o is a commutative ring with 1 which has finitely many maximal ideals {Ai |i ∊ I} and the localization oAi at any maximal ideal Ai is a valuation ring. We assume 2 is a unit in o. Furthermore * denotes an involution on o with the property that there exists a unit θ in o such that θ* = –θ. V is an n-ary free module over o with f : V × V → o a λ-Hermitian form. Thus λ is a fixed element of o with λλ* = 1 and f is a sesquilinear form satisfying f(x, y)* = λf(y, x) for all x, y in V. Assume the form is nonsingular; that is, the mapping M → Hom (M, A) given by x → f( , x) is an isomorphism. In this paper we shall write f(x, y) = xy for x, y in V. 
Ishibashi, Hiroyuki. Generators of Un(V) Over a Quasi Semilocal Semihereditary Ring. Canadian journal of mathematics, Tome 33 (1981) no. 5, pp. 1232-1244. doi: 10.4153/CJM-1981-092-1
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