Universal algebra

by Junpei Sekino

Institution: Oregon State University
Department: Mathematics
Degree: MS
Year: 1968
Keywords: Algebra, Universal
Record ID: 1531898
Full text PDF: http://hdl.handle.net/1957/46575


In this paper, we are concerned with the very general notion of a universal algebra. A universal algebra essentially consists of a set A together with a possibly infinite set of finitary operations on. A. Generally, these operations are related by means of equations, yielding different algebraic structures such as groups, groups with operators, modules, rings, lattices, etc. This theory is concerned with those theorems which are common to all these various algebraic systems. In particular, the fundamental isomorphism and homomorphism theorems are covered, as well as, the Jordan- Holder theorem and the Zassenhaus lemma. Furthermore, new existence proofs are given for sums and free algebras in any primitive class of universal algebras. The last part treats the theory of groups with multi-operators in a manner essentially different from that of P. J. Higgins. The approach taken here generalizes the theorems on groups with operators as found in Jacobson's "Lectures in Abstract Algebra, " vol. I. The basic language of category theory is used whenever convenient.