A precise result on the arithmetic of non-principal orders in algebraic number fields

Philipp A.

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A precise result on the arithmetic of non-principal orders in algebraic number fields

机译：代数数域中非主阶算术的精确结果

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Let R be an order in an algebraic number field. If R is a principal order, then many explicit results on its arithmetic are available. Among others, R is half-factorial if and only if the class group of R has at most two elements. Much less is known for non-principal orders. Using a new semigroup theoretical approach, we study half-factoriality and further arithmetical properties for non-principal orders in algebraic number fields.

机译：令R为代数数字段中的阶数。如果R是主要阶数，则可获得许多关于其算术的显式结果。其中，当且仅当R的类别组最多具有两个元素时，R才是半阶乘。对于非主要订单而言，所知甚少。使用一种新的半群理论方法，我们研究了代数数域中非主阶的半阶乘性和进一步的算术性质。

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《Journal of algebra and its applications》 |2012年第5期|共42页
作者
Philipp A.;
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正文语种 eng
中图分类代数、数论、组合理论;
关键词
algebraic number fields; half-factoriality; non-principal orders; Non-unique factorizations;

机译：代数数域半阶乘非本金阶非唯一因式分解;

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1. A precise result on the arithmetic of non-principal orders in algebraic number fields [J] . Philipp A. Journal of algebra and its applications . 2012,第5期

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2. Efficient Arithmetic in Successive Algebraic Extension Fields Using Symmetries [J] . Sébastien Orange, Guénaël Renault, Kazuhiro Yokoyama Mathematics in Computer Science . 2012,第3期

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3. Efficient Arithmetic in Successive Algebraic Extension Fields Using Symmetries [J] . Orange S., Renault G., Yokoyama K. Mathematics in computer science . 2012,第3期

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A precise result on the arithmetic of non-principal orders in algebraic number fields

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