منابع مشابه
ϕ-ALMOST DEDEKIND RINGS AND $\Phi$-ALMOST DEDEKIND MODULES
The purpose of this paper is to introduce some new classes of rings and modules that are closely related to the classes of almost Dedekind domains and almost Dedekind modules. We introduce the concepts of $\phi$-almost Dedekind rings and $\Phi$-almost Dedekind modules and study some properties of this classes. In this paper we get some equivalent conditions for $\phi$-almost Dedekind rings and ...
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We give an affirmative answer to a 1976 question of M. Rosen: every abelian group is isomorphic to the class group of an elliptic Dedekind domain R. We can choose R to be the integral closure of a PID in a separable quadratic field extension. In particular, this yields new and – we feel – simpler proofs of theorems of L. Claborn and C.R. Leedham-Green. Luther Claborn received his PhD from U. Mi...
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During the last 100 to 150 years, it has become common practice for mathematicians to consider collecting numbers (and/or other objects) into a single conglomerate. This point of view in fact permeates much of higher level mathematics. As such, students of mathematics should have a rm grip on the underlying ideas of how these conglomerates behave. These conglomerates are typically called sets ...
متن کاملHigher Dimensional Dedekind Sums
In this paper we will study the number-theoretical properties of the expression v1 nkal rcka,, d(p; a I . . . . . an) = ( 1) n/2 ~ cot cot (1) k=l P P and of related finite trigonometric sums. In Eq. (I), p is a positive integer, a~ . . . . . a, are integers prime to p, and n is even (for n odd the sum is clearly equal to zero). There are two reasons for being interested in sums of this type. F...
متن کاملFactoring after Dedekind
Let K be a number field and p be a prime number. When we factor (p) = pOK into prime ideals, say (p) = p1 1 · · · p eg g , we refer to the data of the ei’s, the exponents fi in the norms Npi = p fi , and g (the number of pi’s), as the “shape” of the factorization of (p). (What we are leaving out of this is explicit information about generators for the ideals pi.) Similarly, if a monic polynomia...
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ژورنال
عنوان ژورنال: Nature
سال: 1916
ISSN: 0028-0836,1476-4687
DOI: 10.1038/097103b0