Upper bounds on the sizes of finitely generated algebras

• Autorzy: Berman J.
• Języki publikacji: EN

Abstrakty

EN

We present an upper bound for the cardinality of any n-generated algebra in a locally finite variety V of algebras. This upper bound depends only on some fundamental numerical invariants of the n-generated subdirectly irreducible algebras in V. A theorem characterizing those varieties that contain algebras whose cardinalities achieve the upper bound is proved. Several explicit methods for computing the exact values of these invariants are described. The final section contains detailed concrete examples illustrating applications of the characterization theorem and of the various methods for computing the upper bound.

Słowa kluczowe

EN

arithmetical variety; free algebra; valuation; semisimple algebra; finitely generated; Möbius function

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2011
• Tom: Vol. 44, nr 3
• Strony: 447--471
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Berman J.

• Department Of Mathematics Statistics, And Computer Science University Of Illinois At Chicago 851 S. Morgan Street Chicago, Il, USA,

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