{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:29:40Z","timestamp":1760149780782,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,8,28]],"date-time":"2023-08-28T00:00:00Z","timestamp":1693180800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>An ideal projector on the space of polynomials C[x]=C[x1,\u2026,xd] is a projector whose kernel is an ideal in C[x]. Every ideal projector P can be written as a sum of ideal projectors P(k) such that the intersection of their kernels kerP(k) is a primary decomposition of the ideal kerP. In this paper, we show that P is a limit of Lagrange projectors if and only if each P(k) is. 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