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Group and Geometric Quotient Semiproducts

In: Simple Relation Algebras

Author

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  • Steven Givant

    (Mills College, Department of Mathematics)

  • Hajnal Andréka

    (Alfréd Rényi Institute of Mathematics, Institute of Mathematics, Hungarian Academy of Sciences)

Abstract

This chapter presents two concrete examples of the quotient semiproduct construction from Chapter 8 In the first example, the base algebras are algebras of subsets, or complexes, of groups under the usual set-theoretic Boolean operations and the relative operations induced by the group operations on complexes. I n the second example, the base algebras are algebras of complexes of projective geometries (augmented by an identity element) under the set-theoretic Boolean operations and the relative operations induced by the collinearity relation. In both cases, it is shown that a quotient semiproduct system can always be reduced to a corresponding system consisting of groups and group quotient isomorphisms, or geometries and geometric quotient isomorphisms, respectively. This reduction leads to substantial simplifications in terminology and notation.

Suggested Citation

  • Steven Givant & Hajnal Andréka, 2017. "Group and Geometric Quotient Semiproducts," Springer Books, in: Simple Relation Algebras, chapter 0, pages 321-406, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-67696-8_9
    DOI: 10.1007/978-3-319-67696-8_9
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