Geodesic
Radical Regularity in Differential Rings
Canadian journal of mathematics, Tome 23 (1971) no. 2, pp. 197-201

Voir la notice de l'article provenant de la source Cambridge University Press

In [1], we discussed completions of differentially finitely generated modules over a differential ring R. It was necessary that the topology of the module be induced by a differential ideal of R and it was natural that this ideal be contained in J(R), the Jacobson radical of R. The ideal to be chosen, called Jd(R), was the intersection of those ideals which are maximal among the differential ideals of R. The question as to when Jd(R) ⊆ J(R) led to the definition of a class of rings called radically regular rings. These rings do satisfy the inclusion, and we showed in [1, Theorem 2] that R could always be “extended”, via localization, to a radically regular ring in such a way as to preserve all its differential prime ideals.In the present paper, we discuss the stability of radical regularity under quotient maps, localization, adjunction of a differential indeterminate, and integral extensions. 
Gorman, Howard E. Radical Regularity in Differential Rings. Canadian journal of mathematics, Tome 23 (1971) no. 2, pp. 197-201. doi: 10.4153/CJM-1971-019-7
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[1] 1. Gorman, H. E., Differential rings and modules (to appear in Scripta Math.). Google Scholar

[2] 2. Kaplansky, I., An introduction to differential algebra, Actualités Sci. Indust., No. 1251 = Publ. Inst. Math. Univ. Nancago, No. 5 (Hermann, Paris, 1957). Google Scholar

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