An arithmetic obstruction to division algebra decomposability
نویسندگان
چکیده
منابع مشابه
Reducing Ideal Arithmetic to Linear Algebra Problems
In this paper, we will show a reduction of ideal arithmetic, or more generally, of arithmetic of ZZ{modules of full rank in orders of number elds to problems of linear algebra over ZZ=mZZ, where m is a possibly composite integer. The problems of linear algebra over ZZ=mZZ will be solved directly, instead of either \reducing" them to problems of linear algebra over ZZ or factoring m and working ...
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where z is an integer then gcd(a, b) = gcd(b, c). Indeed any divisor of a and b will divide c, and conversely any divisor of b and c will divide a. We can compute c by taking the remainder after dividing a by b, i.e. c is a mod b. (We will discuss the mod operation in greater details in the next section, but at this point, we only need the definition of c as the remainder of dividing a by b.) B...
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The purpose of this paper is to study the tropical algebra – the algebra over the tropical semi-ring. We start by introducing a third approach to arithmetic over the max-plus semi-ring which generalizes the two other concepts in use. Regarding this new arithmetic, matters of tropical matrices are discussed and the properties of these matrices are studied. These are the preceding phases toward t...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2000
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-00-05296-5