Irreducible polynomials which are locally reducible everywhere期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Irreducible polynomials which are locally reducible everywhere

Authors:	Robert Guralnick Murray M Schacher Jack Sonn

Institution:	Department of Mathematics, University of Southern California, Los Angeles, California 90089-2532 ; Department of Mathematics, University of California at Los Angeles, Los Angeles, California 90024 ; Department of Mathematics, Technion, 32000 Haifa, Israel

Abstract:	For any positive integer , there exist polynomials $f(x)\in \mathbb{Z} x]$ of degree which are irreducible over $\mathbb{Q}$ and reducible over $\mathbb{Q} _{p}$ for all primes if and only if is composite. In fact, this result holds over arbitrary global fields.

Keywords:

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文