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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Word problem for ringoids of numerical functions


Author: A. Iskander
Journal: Trans. Amer. Math. Soc. 158 (1971), 399-408
MSC: Primary 02.75; Secondary 08.00
DOI: https://doi.org/10.1090/S0002-9947-1971-0280375-3
MathSciNet review: 0280375
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Abstract: A. The composition ringoid of functions on (i) the positive integers, (ii) all integers, (iii) the reals and (iv) the complex numbers, do not satisfy any identities other than those satisfied by all composition ringoids.

B. Given two words $ u,\upsilon $ of the free ringoid, specific functions on the positive integers, $ {f_1}, \ldots ,{f_k}$ can be described such that $ u({f_1}, \ldots ,{f_k})$ and $ \upsilon ({f_1}, \ldots ,{f_k})$, evaluated at 1, are equal iff $ u = \upsilon $ is an identity of the free ringoid.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0280375-3
Keywords: Semiring, free composition ringoid, functional extension, functions with finite range, canonical forms, depth, width, rank, algorithm
Article copyright: © Copyright 1971 American Mathematical Society

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