(countable, set theory, analysis) A collection of subsets of a given set, such that this collection contains the empty set, and the collection is closed under unions and complements (and thereby also under intersections and differences).
(figuratively) A system or process, that is like algebra by substituting one thing for another, or in using signs, symbols, etc., to represent concepts or ideas.
“As part of their strategy to build up the mathematics department, they appointed an algebraist to a Readership, and two other staff to Lecturerships.”