We generalize to universal algebra concepts originating from lambda calculus and programming in order first to prove a new result on the lattice of λ-theories, and second a general theorem of pure universal algebra which can be seen as a meta version of the Stone Representation Theorem. The interest of a systematic study of the lattice λT of λ-theories grows out of several open problems on lamb...

A general method is presented for establishing universal factorization equalities for 2×2 and 4×4 block matrices. As applications, some universal factorization equalities for matrices over four-dimensional algebras are established, in particular, over the Hamiltonian quaternion algebra.

A class F of universal algebras is called a formation if the following conditions are satisfied: 1) Any homomorphic image of A ∈ F is in F ; 2) If α1, α2 are congruences on A and A/αi ∈ F , i = 1, 2, then A/(α1∩ α2) ∈ F . We prove that any formation generated by a simple algebra with permutable congruences is minimal, and hence any formation containing a simple algebra, with permutable congruen...