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In this paper we give a generalization of the notion—introduced by C. Traverso in [5]— of “glueing of prime ideals of a ring over a prime ideal of a ring ”. We prove the following result: if is an overring of , integral of finite type over , can be obtained from by a finite number of glueings of the above defined kind; geometrically, every singularity of an algebraic variety can be obtained from the normalization of , by a finite number of such glueings.
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