Vol. 20, No. 1, 1967

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Residuated mappings

Jean-Claude B. Derderian

Vol. 20 (1967), No. 1, 35–43

In a series of papers, D. J. Foulis developed a theory in the course of which he obtained analogues of Von Neumann’s Coordinatization Theorem by making use of -monotone mappings. A generalization of these mappings, residuated mappings, leads to extensions of his results. Residuated mappings also arise independently in studies of R. Croisot and G. Nöbeling. The purpose of this paper is to develop their properties systematically. Of particular help is the link established with the basic properties of M-homomorphisms between groups with operators yielding analogues of the Fundamental Theorem of Homomorphisms and Fitting’s Lemma, and with the study of residuation especially in Noetherian rings.

Mathematical Subject Classification
Primary: 06.20
Received: 15 December 1965
Published: 1 January 1967
Jean-Claude B. Derderian