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On the global dimension of an algebra (1973)

Govorov, V. E.

Springer

Mathematical notes 14 (1973), S. 789-792

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ISSN: 1573-8876

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract Let algebra R = Λ/P, where Λ is a free algebra over a field w. gl. dim R: = {min n ¦∀ R-modules X, Y, Tor n+1 R (X, Y)=0}. In order that w. gl. dim R≤2n (w. gl. dim R≤2n+1), it is necessary and sufficient that, for any two ideals of algebra Λ, a left ideal A and a right ideal B, containing ideal P, the following equation holds: $$AP^n \cap P^n B = AP^n B + P^{n + 1} (AP^n B \cap P^{n + 1} = AP^{n + 1} + P^{n + 1} B).$$

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01147457

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