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Finite-valued algebraic lattices

✍ Scribed by J. T. Snodgrass; C. Tsinakis


Publisher
Springer
Year
1993
Tongue
English
Weight
414 KB
Volume
30
Category
Article
ISSN
0002-5240

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πŸ“œ SIMILAR VOLUMES


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We prove that if A is a non-associative algebra over the field of real numbers, if 5 5 5 5 5 5 5 5 there is a norm ΠΈ on A satisfying xy s x y for all x, y in A, and if every one-generated subalgebra of A is finite-dimensional, then A is finite-dimensional.

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We prove that for every ΓΏnite homogeneous e ect algebra E there exists a ΓΏnite orthoalgebra O(E) and a surjective full morphism E : O(E) β†’ E. If E is lattice ordered, then O(E) is an orthomodular lattice. Moreover, E preserves blocks in both directions: the (pre)image of a block is always a block.