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Joins and Direct Products of Equational Classes

Published online by Cambridge University Press:  20 November 2018

G. Grätzer ,
H. Lakser  and
J. Płonka
G. Grätzer
Affiliation:
University of Manitoba
H. Lakser
Affiliation:
University of Manitoba
J. Płonka
Affiliation:
University of Manitoba
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Let K0 and K1 be equational classes of algebras of the same type. The smallest equational class K containing K0 and K1 is the join of K0 and K1; in notation, K = K0 ∨ K1. The direct product K0 × K1 is the class of all algebras α which are isomorphic to an algebra of the form a0 × a1, a0 ∈ K1. Naturally, K0 × K1 ⊆ K0 ∨ K1, Our first theorem states a very simple condition under which K0 × K1 = K0 ∨ K1, and an additional condition under which the representation α ∨ a0 × a1 unique.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 6 , December 1969 , pp. 741 - 744
Copyright
Copyright © Canadian Mathematical Society 1969

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