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On Meromorphisms of Algebraic Systems

Published online by Cambridge University Press:  22 January 2016

Junji Hashimoto
Junji Hashimoto*
Affiliation:
Department of Mathematics, Kobe University
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In the present paper by an algebraic system (algebra) A we shall mean a system with a set F of operations fλ : (x 1,…, xn ) ∈ A × · · · × A → fλ (x 1,…, xn ) ∈ A. A polynomial p(x1, …, xr ) is a function of variables x1 ,…, xr which is either one of the xi , or (recursively) a result of some operation fλ (p 1,…, pn ) performed on other polynomials pi . An algebra A may satisfy a set R of identities p(x1 ,…, xr ) = q(x 1,…, xs ), and then A shall be called an (F, R)-algebra.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 2 , July 1966, pp. 559 - 569
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Hashimoto, J.: Congruence relations and congruence classes in lattices, Osaka Math. J. 15 (1963).Google Scholar
[2] Malcev, A. I.: On the general theory of algebraic systems, Mat. Sb. N. S. 35 (77) (1954), Amer. Math. Soc. Transl. (2) 27 (1963).Google Scholar
[3] Nakayama, T.: Sets, topologies and algebraic systems (Shugo, Iso, Daisukei in Japanese), Tokyo, 1949.Google Scholar
[4] Shoda, K.: Universal theory for algebra (Daisugaku Tsuron in Japanese), Tokyo, 1947.Google Scholar
[5] Shoda, K.: Uber die allgemeinen algebraischen Systeme I-VII, Proc. Imp. Acad. Tokyo 17–20 (1941–4).Google Scholar