Lattices and Ordered Algebraic Structuresby T. S. Blyth
β Scribed by Review by: John M. Howie
- Book ID
- 124944360
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 2006
- Tongue
- English
- Weight
- 327 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0036-1445
- DOI
- 10.2307/20453770
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π SIMILAR VOLUMES
lattices And Ordered Algebraic Structures Provides A Lucid And Concise Introduction To The Basic Results Concerning The Notion Of An Order. Although As A Whole It Is Mainly Intended For Beginning Postgraduates, The Prerequisities Are Minimal And Selected Parts Can Profitably Be Used To Broaden The H
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.
A class of lattice ordered groups is called a formation if it is closed with respect to homomorphic images and finite subdirect products. Analogously we define the formation of GMV -algebras. Let us denote by F 1 and F 2 the collection of all formations of lattice ordered groups or of GMV -algebras,