Word problem for ringoids of numerical functions

Iskander, A.

doi:10.1090/S0002-9947-1971-0280375-3

Word problem for ringoids of numerical functions
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by A. Iskander

Trans. Amer. Math. Soc. 158 (1971), 399-408

DOI: https://doi.org/10.1090/S0002-9947-1971-0280375-3

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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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