منابع مشابه
Factoring 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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In a historical overview, Cristian S. Calude, Elena Calude, and Solomon Marcus identify eight stages in the development of the concept of a mathematical proof in support of an ambitious conjecture: we can express classical mathematical concepts adequately only in a mathematical language in which both truth and provability are essentially unverifiable. In this essay we show, first, that the conc...
متن کاملDedekind Sums with Arguments Near Euler ’ s Number e
We study the asymptotic behaviour of the classical Dedekind sums s(m/n) for convergents m/n of e, e2, and (e+1)/(e−1), where e = 2.71828 . . . is Euler’s number. Our main tool is the Barkan-Hickerson-Knuth formula, which yields a precise description of what happens in all cases.
متن کاملϕ-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 ...
متن کاملOn the Representability Number of Lexicographic Products in a Dedekind-Complete Chain
For any two linear orderings L and M , the representability number reprM (L) of L in M is the least ordinal α such that L can be orderembedded into the lexicographic power Mα lex. We study reprM (L) in the particular case that L is a lexicographic product and M is a Dedekindcomplete chain. Mathematics Subject Classification: Primary: 06A05; Secondary: 03E05, 54F05, 91B16
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1935
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1935-06127-0