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(1975) The logico-algebraic approach to quantum mechanics I, Dordrecht, Springer.
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.
Publication details
DOI: 10.1007/978-94-010-1795-4_9
Full citation:
Foulis, D. J. (1975)., Baer *-semigroups, in C. A. Hooker (ed.), The logico-algebraic approach to quantum mechanics I, Dordrecht, Springer, pp. 141-148.
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