Varieties of idempotent groupoids with small clones
J. Gałuszka (1999)
Colloquium Mathematicae
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We give an equational description of all idempotent groupoids with at most three essentially n-ary term operations.
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Displaying similar documents to “A characterization of modular lattices”
Varieties of idempotent groupoids with small clones
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The main result of this paper is a description of totally commutative idempotent groupoids. In particular, we show that if an idempotent groupoid (G,·) has precisely m ≥ 2 distinct essentially binary polynomials and they are all commutative, then G contains a subgroupoid isomorphic to the groupoid described below. In [2], this fact was proved for m = 2.
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The binary set {0, 1} together with modulo-2 addition and multiplication is called a binary field, which is denoted by F2. The binary field F2 is defined in [1]. A vector space over F2 is called a binary vector space. The set of all binary vectors of length n forms an n-dimensional vector space Vn over F2. Binary fields and n-dimensional binary vector spaces play an important role in practical computer science, for example, coding theory [15] and cryptology. In cryptology, binary fields...
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