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DEFINITION of 'Boolean Algebra'. A division of mathematics which deals with operations on logical values. Boolean algebra traces its origins to an 1854 book by mathematician George Boole. The distinguishing factor of Boolean algebra is that it deals only with the study of binary variables. Most commonly boolean variables are presented with the possible values of 1 (true) or 0 (false).
Cluster algebras are a class of commutative rings introduced by Fomin and Zelevinsky (2002, 2003, 2007). A cluster algebra of rank n is an integral domain A, together with some subsets of size n called clusters whose union generates the algebra A and which satisfy various conditions.luster algebras of rank 2 [edit]. Suppose that we start with the cluster { x 1, x 2 } and take the exchange matrix with b 12 =âb 21 =1. Then mutation gives a sequence of variables x 1, x 2, x 3, x 4 ,... such that the clusters are given by adjacent pairs { x n, x n+1 }.