Abstract
Relational composition is an associative operation; therefore semigroup considerations often help in relational algebra. We study here some less known such effects and relate them with maximal rectangles inside a relation, i.e., with the basis of concept lattice considerations. The set of points contained in precisely one maximal rectangle makes up the fringe. We show that the converse of the fringe sometimes acts as a generalized inverse of a relation. Regular relations have a generalized inverse. They may be characterized by an algebraic condition.
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Schmidt, G. (2008). Rectangles, Fringes, and Inverses. In: Berghammer, R., Möller, B., Struth, G. (eds) Relations and Kleene Algebra in Computer Science. RelMiCS 2008. Lecture Notes in Computer Science, vol 4988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78913-0_26
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DOI: https://doi.org/10.1007/978-3-540-78913-0_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78912-3
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