On a multiplication decomposition theorem in a Dedekind $\sigma$-complete partially ordered linear algebra
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- by Taen Yu Dai PDF
- Proc. Amer. Math. Soc. 44 (1974), 12-16 Request permission
Abstract:
Suppose a Dedekind $\sigma$-complete partially ordered linear algebra (dsc-pola) satisfies a certain multiplication decomposition property (see definition below), then we show that this partially ordered linear algebra actually has the same structure of a special class of real matrix algebras, consisting of elements that can be decomposed as diagonal part plus nilpotent part $w$, such that ${w^2} = 0$.References
- Garrett Birkhoff, Lattice theory, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053
- Taen-yu Dai, On some special classes of partially ordered linear algebras, J. Math. Anal. Appl. 40 (1972), 649–682. MR 316342, DOI 10.1016/0022-247X(72)90011-X
- Ralph DeMarr, On partially ordering operator algebras, Canadian J. Math. 19 (1967), 636–643. MR 212579, DOI 10.4153/CJM-1967-057-6
- Ralph DeMarr, A class of partially ordered linear algebras, Proc. Amer. Math. Soc. 39 (1973), 255–260. MR 313161, DOI 10.1090/S0002-9939-1973-0313161-3
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 44 (1974), 12-16
- MSC: Primary 06A70
- DOI: https://doi.org/10.1090/S0002-9939-1974-0335393-1
- MathSciNet review: 0335393