Tangential idealizers and differential ideals

• Autores: Cleto B. Miranda Neto
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 67, Fasc. 2, 2016, págs. 311-328
• Idioma: inglés
• DOI: 10.1007/s13348-015-0134-2
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• Resumen

  • Our main goal in this note is to give a characteristic-free, general version of Seidenberg’s well-known theorem on the existence of primary decomposition in the class of differential ideals in commutative Noetherian rings containing the rational numbers. Our approach is through the study of general logarithmic derivation modules, here dubbed tangential idealizers, and we first provide a primary decomposition of the tangential idealizer of any given ideal without embedded primary component. Also, we describe a large class of ideals whose radical as well as ordinary and symbolic powers possess the same tangential idealizer, extending a (real analytic) study due to Hauser and Risler. Other results are obtained; for instance, we show that the symbolic powers and the content ideal of a differential ideal are differential as well.