Iterative characterizations of Boolean algebras
β Scribed by Dan Simovici; Corina Reischer
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 240 KB
- Volume
- 15
- Category
- Article
- ISSN
- 0166-218X
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π SIMILAR VOLUMES
The representation of algebras by Boolean products is a very general problem in universal algebra. In this paper we shall characterize the Boolean products of BL-chains, the weak Boolean products of local BL-algebras, and the weak Boolean products of perfect BL-algebras.
We consider eight special kinds of subalgebras of Boolean algebras. In Section 1 we describe the relationships between these subalgebra notions. In succeeding sections we consider how the subalgebra notions behave with respect to the most common cardinal functions on Boolean algebras.
In this paper, the (weak) Boolean representation of R0-algebras are investigated. In particular, we show that directly indecomposable R0-algebras are equivalent to local R0-algebras and any nontrivial R0-algebra is representable as a weak Boolean product of local R0-algebras.