Abstract
Modern mathematics is replete with instances of semigroups S which are equipped with involutory antiautomorphisms *:S→S, two noteworthy examples being multiplicative groups on the one hand, and the multiplicative semigroups of Baer *-rings [1, Chapter III, Definition 2] on the other. In this paper we take the second example cited above as our point of departure, setting forth certain postulates which determine what we will call a Baer “-semigroup, and showing that such semigroups provide a more or less natural “coordinatization” of the orthocomplemented weakly modular lattices employed by Loomis [2] in his version of the dimension theory of operator algebras.
This paper contains part of the author’s doctoral dissertation (Tulane, 1958), written under the direction of Professor F. B. Wright.
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Bibliography
Kaplansky, I., Rings of Operators, University of Chicago Mimeographed Notes, 1955.
Loomis, L. H., The Lattice Theoretic Background of the Dimension Theory of Operator Algebras’, Memoirs Amer. Math. Soc., No. 18, 1955.
Halmos, P. R., ‘Algebraic Logic, I, Monadic Boolean Algebras, Compositio Math. 12 (1955), 217–249.
von Neumann, J., Continuous Geometry. Parts I, II, III, Princeton University Planographed Notes, 1937.
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© 1975 D. Reidel Publishing Company, Dordrecht, Holland
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Foulis, D.J. (1975). Baer *-Semigroups. In: Hooker, C.A. (eds) The Logico-Algebraic Approach to Quantum Mechanics. The University of Western Ontario Series in Philosophy of Science, vol 5a. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1795-4_9
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DOI: https://doi.org/10.1007/978-94-010-1795-4_9
Publisher Name: Springer, Dordrecht
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