WebAug 16, 2024 · For example, every quotient ring of a Hilbert–Jacobson ring is itself Hilbert–Jacobson, so that for this property any ideal property must hold for every ideal in a Hilbert–Jacobson ring. ac.commutative-algebra; ideals; Share. Cite. Improve this question. Follow asked Aug 16, 2024 at 17:10. WebAug 1, 1975 · A ring R is said to be a Jacobson ring if, in every homomorphic image of R, the Jacobson radical coincides with the prime radical. Equiv- alently every prime ideal of R is an intersection of primitive ideals, that is, is a semiprimitive ideal. ... Hilbert rings and the Hilbert nullstellensatz. Math. Z., 54 (1951), pp. 136-140. View Record in ...
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Jacobsen-rings and Hilbert algebras with polynomial identities …
WebExamples. The prototypical example of a Banach algebra is (), the space of (complex-valued) continuous functions on a locally compact space that vanish at infinity. is unital if and only if is compact.The complex conjugation being an involution, () is in fact a C*-algebra.More generally, every C*-algebra is a Banach algebra by definition. The set of real … Web会员中心. vip福利社. vip免费专区. vip专属特权 In algebra, a Hilbert ring or a Jacobson ring is a ring such that every prime ideal is an intersection of primitive ideals. For commutative rings primitive ideals are the same as maximal ideals so in this case a Jacobson ring is one in which every prime ideal is an intersection of maximal ideals. Jacobson rings were introduced independently by Wolfgang Krull (1951, 1952), who named them after Nathan Jacobson because of their relation to Jacobson radicals, and by Oscar Goldman (195… buddy system music 2016