Ewa Graczyńska, Dietmar Schweigert
Abstract
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We invent the notion of a {\it dimension of a variety} $V$ as the cardinality of all its proper {\it derived} subvarieties (of the same type). The dimensions of varieties of lattices, varieties of regular bands and other general algebraic structures are determined.
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We invent the notion of a {\it dimension of a variety} $V$ as the cardinality of all its proper {\it derived} subvarieties (of the same type). The dimensions of varieties of lattices, varieties of regular bands and other general algebraic structures are determined.
Key concepts: Variety (cybernetics), Dimension (graph theory), Cardinality (data modeling), Algebraic variety, Mathematics, Algebraic number, Pure mathematics, Algebra over a field