ALGEBRAIC PROPERTIES OF WEAK PERRON NUMBERS
نویسندگان
چکیده
منابع مشابه
Algebraic Properties of Weak Perron Numbers
We study algebraic properties of real positive algebraic numbers which are not less than the moduli of their conjugates. In particular, we are interested in the relation of these numbers to Perron numbers.
متن کاملAlgebraic properties of external numbers
Neutrices and external numbers were proposed as models of orders of magnitude within nonstandard analysis. We show that the external numbers form a commutative regular semigroup for addition and that the external numbers which are not neutrices form a commutative regular semigroup for multiplication. The validity of the distributive law is restricted, but it can be fully characterized. 2000 Mat...
متن کاملThe smallest Perron numbers
A Perron number is a real algebraic integer α of degree d ≥ 2, whose conjugates are αi, such that α > max2≤i≤d |αi|. In this paper we compute the smallest Perron numbers of degree d ≤ 24 and verify that they all satisfy the Lind-Boyd conjecture. Moreover, the smallest Perron numbers of degree 17 and 23 give the smallest house for these degrees. The computations use a family of explicit auxiliar...
متن کاملAlgebraic Perron-Frobenlus Theory
Let V be a vector space over a fully ordered field F. In Sec. 2 we characterize cones K with ascending chain condition (ACC) on faces of Ii. In Sec. 3 we show that if K has ACC on faces, then an operator A is strongly irreducible if and only if A is irreducible. In Sec. 4 we prove theorems of Perron-Frobenius type for a strongly irreducible operator A in the case that FR, the real field, and K ...
متن کاملQuestions about algebraic properties of real numbers
This paper is a survey of natural questions (with few answers) arising when one wants to study algebraic properties of real numbers, i.e., properties of real numbers w.r.t. {+, −, ×, >, ≥} in a constructive setting. Introduction This paper is a survey of natural questions (with few answers) arising when one wants to study algebraic properties of real numbers, i.e., properties of real numbers w....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Tatra Mountains Mathematical Publications
سال: 2013
ISSN: 1210-3195
DOI: 10.2478/tmmp-2013-0023