Vol. 22, No. 1, 1967

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Limits in certain classes of abstract algebras

Gloria Conyers Hewitt

Vol. 22 (1967), No. 1, 109–115

This paper is primarily concerned with the existence of direct limits in certain classes of Boolean algebras. The concepts of inverse and direct limits are defined relative to a class A of abstract algebras . It is assumed that the algebras in A are of the same type.

It is found that classes which are closed under such constructions as the formation of homomorphic images, subalgebras, free products and free unions do admit direct and inverse limits. In fact, the existence of direct limits is closely related to the existence of free products and dually, the existence of inverse limits is related to the existence of free unions. Also there is a relationship between the existence of inverse limits and direct limits.

Mathematical Subject Classification
Primary: 08.10
Received: 23 May 1966
Published: 1 July 1967
Gloria Conyers Hewitt