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Transactions of the American Mathematical Society

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A bound on the rank of purely simple systems


Author: Frank Okoh
Journal: Trans. Amer. Math. Soc. 232 (1977), 169-186
MSC: Primary 15A03; Secondary 13F10
DOI: https://doi.org/10.1090/S0002-9947-1977-0498625-2
MathSciNet review: 0498625
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1977-0498625-2
Keywords: Torsion-free system, torsion-closure, pure projective, purely simple, basis with respect to generation, rank
Article copyright: © Copyright 1977 American Mathematical Society

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