Minimal Characteristic Algebras for Rectangular k - Normal Identities
نویسندگان
چکیده
A characteristic algebra for a hereditary property of identities of a fixed type τ is an algebra A such that for any variety V of type τ , we have A ∈ V if and only if every identity satisfied by V has the property p. This is equivalent to A being a generator for the variety determined by all identities of type τ which have property p. PÃlonka has produced minimal (smallest cardinality) characteristic algebras for a number of hereditary properties, including regularity, normality, uniformity, biregularity, rightand leftmost, outermost, and external-compatibility. In this paper, we use a construction of PÃlonka to study minimal characteristic algebras for the property of rectangular k-normality. In particular, we construct minimal characteristic algebras of type (2) for k-normality and rectangularity for 1 ≤ k ≤ 3. 2000 Mathematics Subject Classification: 08A05, 08B05
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