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Ideals of the associative algebra operad

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arxiv 2307.07669 v2 pith:GDSOKVNN submitted 2023-07-15 math.RA

Y.-H. Bao , J.-N. Xu , Y. Ye , J. J. Zhang , Y.-F. Zhang This is my paper
classification math.RA
keywords idealsoperadoperadicalgebraassociativeconsequencecorrespondenceelement
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abstract

We prove a one-to-one correspondence between the operadic ideals of the operad $\As$ and $T$-ideals. As a consequence, we show that $\As$ is noetherian and that every proper operadic ideal of $\ias$ is generated by a single element.

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