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Bavula","submitted_at":"2011-04-03T19:56:00Z","abstract_excerpt":"In contrast to its subalgebra $A_n:=K<x_1, ..., x_n, \\frac{\\der}{\\der x_1}, ...,\\frac{\\der}{\\der x_n}>$ of polynomial differential operators (i.e. the $n$'th Weyl algebra), the algebra $\\mI_n:=K<x_1, ..., x_n, \\frac{\\der}{\\der x_1}, ...,\\frac{\\der}{\\der x_n}, \\int_1, ..., \\int_n>$ of polynomial integro-differential operators is neither left nor right Noetherian algebra; moreover it contains infinite direct sums of nonzero left and right ideals. 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