A bound on the rank of purely simple systems

Okoh, Frank

doi:10.1090/S0002-9947-1977-0498625-2

A bound on the rank of purely simple systems
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Trans. Amer. Math. Soc. 232 (1977), 169-186 Request permission

Abstract:

A pair of complex vector spaces (V, W) is called a system if and only if there is a C-bilinear map from ${{\mathbf {C}}^2} \times V$ to W. The category of systems contains subcategories equivalent to the category of modules over the ring of complex polynomials. Many concepts in the latter generalize to the category of systems. In this paper the pure projective systems are characterized and a bound on the rank of purely simple systems is obtained.

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