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Formations of lattice ordered groups and ofGMV-algebras

✍ Scribed by Ján Jakubík

Book ID
111492977
Publisher
SP Versita
Year
2008
Tongue
English
Weight
203 KB
Volume
58
Category
Article
ISSN
0139-9918

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✦ Synopsis

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, respectively. Both F 1 and F 2 are partially ordered by the class-theoretical inclusion. We prove that F 1 satisfies the infinite distributivity law X ∧ i∈I X i = i∈I (X ∧X i ) and that F 2 is isomorphic to a principal ideal of F 1 .

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✍ Ján Jakubík 📂 Article 📅 2007 🏛 SP Versita 🌐 English ⚖ 159 KB

The notion of internal subdirect decomposition can be defined in each variety of algebras. In the present note we prove the validity of a cancellation rule concerning such decompositions for lattice ordered groups and for GMV -algebras. For the case of groups, this cancellation rule fails to be vali