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Classes of Functions on Algebras

  • C. G. Cullen (a1) and C. A. Hall (a1)

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Let be a finite-dimensional linear associative algebra over the real field R or the complex field C and let F be a function with domain and range in .

Several classes of functions on have been discussed in the literature, and it is the purpose of this paper to discuss the relationships between these classes and to present some interesting examples. First we shall list the definitions of the classes we wish to consider here.

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References

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1. Cullen, C. G., Intrinsic functions on matrices of real quaternions, Can. J. Math. 15 (1963) 456466.
2. Cullen, C. G. and Hall, C. A., Functions on semi-simple algebras, To appear in Amer. Math. Monthly.
3. Jacobson, N., Lectures in abstract algebra, vol. II (New York, 1953).
4. Portmann, W. O., A sufficient condition for a matric function to be a primary matric function, Proc. Amer. Math. Soc, 11 (1960), 102106.
5. Rinehart, R. F., Elements of a theory of intrinsic functions on algebras, Duke Math. J. 27 (1960), 119.
6. Rinehart, R. F., Intrinsic functions on matrices, Duke Math. J. 28 (1961), 291300.
7. Wiegmann, N. A., Some theorems on matrices with real quaternion elements, Can. J. Math., 7 (1955), 191201.
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