Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-23T23:51:48.096Z Has data issue: false hasContentIssue false
  • English
  • Français

On Meromorphisms of Algebraic Systems

Published online by Cambridge University Press:  22 January 2016

Junji Hashimoto
Junji Hashimoto*
Affiliation:
Department of Mathematics, Kobe University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In the present paper by an algebraic system (algebra) A we shall mean a system with a set F of operations fλ: (x1,…, xn) ∈ A × · · · × A → fλ(x1,…, 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(p1,…, pn) performed on other polynomials pi. An algebra A may satisfy a set R of identities p(x1,…, xr) = q(x1,…, xs), and then A shall be called an (F, R)-algebra.

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