On many-sorted algebraic closure operators. (English) Zbl 1038.08001

Climent Vidal, Juan; Soliveres Tur, Juan

Math. Nachr. 266, 81-84 (2004).

A well-known theorem of Birkhoff-Frink states that every algebraic closure operator can be realized as the subalgebra operator of an appropriate algebra. However, for many-sorted algebras (i.e. indexed families of sets) an analogous theorem is not longer true. The main theorem of the paper asserts that the corresponding many-sorted closure operators are precisely the uniform algebraic operators.

Reviewer: Radomír Halaš (Prostejov)

MSC:

08A30	Subalgebras, congruence relations
06A15	Galois correspondences, closure operators (in relation to ordered sets)

Keywords:

Many-sorted algebra; support; many-sorted uniform algebraic closure operator