THE ALGEBRA OF IMPLICIT OPERATIONS

• Type: Article in International Scientific Journal
• Date: 1989

Authors

ALMEIDA, J (Author) FCUP

Journal

Title: Algebra Universalis

Vol. 26

Pages: 16-32

ISSN: 0002-5240

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 17 Citations

Scopus - 18 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-001-SVC

DOI: 10.1007/BF01243870

Abstract (EN): For an ordinal ¿ and a class {Mathematical expression} of topological algebras of a given type (which may be infinite and may contain inflnitary operations), an ¿-ary implicit operation on {Mathematical expression} is any "new"¿-ary operation whose introduction does not eliminate any continuous homomorphisms between members of {Mathematical expression}. The set of all ¿-ary implicit operations on {Mathematical expression} is denoted by {Mathematical expression} and forms an algebra of the given type which is endowed with the least topology making continuous all homomorphisms into members of {Mathematical expression}. With this topology, {Mathematical expression} is a topological algebra in which the subalgebra ¿¿ {Mathematical expression} of all ¿-ary operations on {Mathematical expression} which are induced by terms is dense, provided that {Mathematical expression} is closed under the formation of closed subalgebras and finitary direct products. This is obtained by realizing {Mathematical expression} as an inverse limit of ¿-generated members of {Mathematical expression}. These results are applied to pseudovarieties of topological and finite algebras. © 1989 Birkhÿuser Verlag.

Language: English

Type (Professor's evaluation): Scientific