Geodesic
On minimally Free Algebras
Canadian journal of mathematics, Tome 37 (1985) no. 5, pp. 963-978

Voir la notice de l'article provenant de la source Cambridge University Press

For us an “algebra” is a finitary “universal algebra” in the sense of G. Birkhoff [9]. We are concerned in this paper with algebras whose endomorphisms are determined by small subsets. For example, an algebra A is rigid (in the strong sense) if the only endomorphism on A is the identity idA . In this case, the empty set determines the endomorphism set E(A). We place the property of rigidity at the bottom rung of a cardinal-indexed ladder of properties as follows. Given a cardinal number κ, an algebra A is minimally free over a set of cardinality κ (κ-free for short) if there is a subset X ⊂ A of cardinality κ such that every function f:X → A extends to a unique endomorphism φ ∊ E(A). (It is clear that A is rigid if and only if A is 0-free.) Members of X will be called counters; and we will be interested in how badly counters can fail to generate the algebra. 
Bankston, Paul; Schutt, Richard. On minimally Free Algebras. Canadian journal of mathematics, Tome 37 (1985) no. 5, pp. 963-978. doi: 10.4153/CJM-1985-052-8
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