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An operator defined on a set S which takes two elements from S as inputs and returns a single element of S. Binary operators are called compositions by Rosenfeld (1968). Sets ...

The invertible matrix theorem is a theorem in linear algebra which gives a series of equivalent conditions for an n×n square matrix A to have an inverse. In particular, A is ...

A meromorphic function is a single-valued function that is analytic in all but possibly a discrete subset of its domain, and at those singularities it must go to infinity ...

A triangle-replaced graph T(G) is a cubic graph in which each vertex is replaced by a triangle graph such that each vertex of the triangle is connected to one of the ...

Given a real number q>1, the series x=sum_(n=0)^inftya_nq^(-n) is called the q-expansion, or beta-expansion (Parry 1957), of the positive real number x if, for all n>=0, ...

A product of ANDs, denoted ^ _(k=1)^nA_k. The conjunctions of a Boolean algebra A of subsets of cardinality p are the 2^p functions A_lambda= union _(i in lambda)A_i, where ...

In logic, a term is a variable, constant, or the result of acting on variables and constants by function symbols. In algebra, a term is a product of the form x^n (in the ...

The inverse of a square matrix A, sometimes called a reciprocal matrix, is a matrix A^(-1) such that AA^(-1)=I, (1) where I is the identity matrix. Courant and Hilbert (1989, ...

The complete products of a Boolean algebra of subsets generated by a set {A_k}_(k=1)^p of cardinal number p are the 2^p Boolean functions B_1B_2...B_p=B_1 intersection B_2 ...

In the study of non-associative algebra, there are at least two different notions of what the half-Bol identity is. Throughout, let L be an algebraic loop and let x, y, and z ...