An algorithm for constructing a variety of arbitrary finite dimension
Autor: | D. M. Smirnov |
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Rok vydání: | 1998 |
Předmět: | |
Zdroj: | Algebra and Logic. 37:92-100 |
ISSN: | 1573-8302 0002-5232 |
Popis: | The dimension of a variety V of algebras is the greatest length of a basis (i.e., of an independent generating set) for an SC-theory SC(V), consisting of strong Mal'tsev conditions satisfied in V. The variety V is assumed infinite-dimensional if the lengths of the bases in SC(V) are not bounded. A simple algorithm is found for constructing a variety of any finite dimension r≥1. Using the sieve of Eratosthenes, r distinct primes p1, p2,…, pr are written and their product n=p1p2…pr computed. The variety Gn of algebras (A, f) with one n-ary operation satisfying the identity f(x1, x2,…,xn)=f(x2,…,xn, x1) has, then, dimension r. |
Databáze: | OpenAIRE |
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