Displaying similar documents to “Construction of Ray class fields by elliptic units”

Lower powers of elliptic units

Stefan Bettner, Reinhard Schertz (2001)

Journal de théorie des nombres de Bordeaux

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In the previous paper [Sch2] it has been shown that ray class fields over quadratic imaginary number fields can be generated by simple products of singular values of the Klein form defined below. In the present article the second named author has constructed more general products that are contained in ray class fields thereby correcting Theorem 2 of [Sch2]. An algorithm for the computation of the algebraic equations of the numbers in Theorem 1 of this paper has been implemented in a...

A primrose path from Krull to Zorn

Marcel Erné (1995)

Commentationes Mathematicae Universitatis Carolinae

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Given a set X of “indeterminates” and a field F , an ideal in the polynomial ring R = F [ X ] is called conservative if it contains with any polynomial all of its monomials. The map S ↦ R S yields an isomorphism between the power set P ( X ) and the complete lattice of all conservative prime ideals of R . Moreover, the members of any system S ⊆ P ( X ) of finite character are in one-to-one correspondence with the conservative prime ideals contained in P S = ⋃ { R S : S ∈ S } , and the maximal members of S correspond to the maximal ideals contained...

Intersections of minimal prime ideals in the rings of continuous functions

Swapan Kumar Ghosh (2006)

Commentationes Mathematicae Universitatis Carolinae

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A space X is called μ -compact by M. Mandelker if the intersection of all free maximal ideals of C ( X ) coincides with the ring C K ( X ) of all functions in C ( X ) with compact support. In this paper we introduce φ -compact and φ ' -compact spaces and we show that a space is μ -compact if and only if it is both φ -compact and φ ' -compact. We also establish that every space X admits a φ -compactification and a φ ' -compactification. Examples and counterexamples are given.