An algorithm for constructing a variety of arbitrary finite dimension

Autor:	D. M. Smirnov
Rok vydání:	1998
Předmět:	Discrete mathematics Combinatorics Identity (mathematics) Sieve of Eratosthenes Basis (linear algebra) Dimension (vector space) Logic Bounded function Product (mathematics) Generating set of a group Variety (universal algebra) Analysis Mathematics
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
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::03fb3b3ab709c8a811bfa9a2b64a9b16 https://doi.org/10.1007/bf02671595 Zobrazit plný text záznamu Full text from SpringerLink