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首页> 外文期刊>Journal of algebra and its applications >The global dimension of the algebras of polynomial integro-differential operators I-n and the Jacobian algebras A(n)
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The global dimension of the algebras of polynomial integro-differential operators I-n and the Jacobian algebras A(n)

机译：多项式积分差分运算符I-N和雅可比代数A（n）的全局尺寸

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The aim of the paper is to prove two conjectures from the paper [V. V. Bavula, The algebra of integro-differential operators on a polynoral algebra, 1. London Muth. Soc. (2) 83 (2011) 517 543, arXiv:rnath.B. A/0912.07231 that the (left and right) global dimension of the algebra I-n := K < x(1),... x(n), partial derivative/partial derivative x(1),..., partial derivative/partial derivative x(n), integral(1),...,integral(n)} of polynomial integro-differential operators and the Jacobian algebra A(n) is equal to 17, (over a field of characteristic zero). The algebras I-n, and A(n) are neither left nor right Noetherian and I-n subset of A(n). Furthermore, they contain infinite direct sums of nonzero left/right ideals and are not domains. An analogue of Hilbert's Syzygy Theorem is proven for the algebras I-n, A(n), and their factor algebras. It is proven that the global dimension of all prime factor algebras of the algebras I-n, and A(n) is n and the weak global dimension of all the factor algebras of I-n, and A(n) is n.
机译：本文的目的是从论文中证明两个猜想[V. V. Bavula，聚偶数差分运营商的聚偶数算子上的代数，1.伦敦Muth。 SOC。 （2）83（2011）517 543，Arxiv：rnath.b。 A / 0912.07231代数（左右）全局尺寸：= k

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