Orthomodularity and the direct sum of division subrings of the quaternions
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- by Ronald P. Morash PDF
- Proc. Amer. Math. Soc. 36 (1972), 63-68 Request permission
Abstract:
Let D be any division subring of the real quaternions H. Let $\oplus$ D denote the linear space of all finitely nonzero sequences from D and let L denote the lattice of all “$\bot$-closed” subspaces of $\oplus$ D, where “$\bot$” denotes the orthogonality relation derived from the H-valued form $(a,b) = \sum {({a_i}b_i^ \ast :i = 1,2, \cdots )}$ where $a,b \in \oplus D,a = ({a_1},{a_2}, \cdots ,{a_N},0,0, \cdots )$ and $b = ({b_1},{b_2}, \cdots ,{b_M},0,0, \cdots )$, and $b_i^ \ast$ is the quaternionic conjugate of ${b_i}$. Then, the lattice L is complete and orthocomplemented, but is not orthomodular.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 36 (1972), 63-68
- MSC: Primary 46C05; Secondary 16A40
- DOI: https://doi.org/10.1090/S0002-9939-1972-0312225-7
- MathSciNet review: 0312225