• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Journal of Algebra >Power monoids: A bridge between factorization theory and arithmetic combinatorics
【24h】

Power monoids: A bridge between factorization theory and arithmetic combinatorics

机译：电力长台：分解理论与算术组合之间的桥梁

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

We extend a few fundamental aspects of the classical theory of non-unique factorization, as presented in Geroldinger and Halter-Koch's 2006 monograph on the subject, to a non-commutative and non-cancellative setting, in the same spirit of Baeth and Smertnig's work on the factorization theory of non-commutative, but cancellative monoids (Baeth and Smertnig (2015) ). Then, we bring in power monoids and, applying the abstract machinery developed in the first part, we undertake the study of their arithmetic.More in particular, letHbe a multiplicatively written monoid. The setPfin(H)of all non-empty finite subsets ofHis naturally made into a monoid, which we call the power monoid ofHand is non-cancellative unlessHis trivial, by endowing it with the operation(X,Y)?{xy:(x,y)∈X×Y}.Power monoids are, in disguise, one of the primary objects of interest in arithmetic combinatorics, and here for the first time we tackle them from the perspective of factorization theory. Proofs lead to consider various properties of finite subsets ofNthat can or cannot be split into a sumset in a non-trivial way, giving rise to a rich interplay with additive number theory.
机译：我们延长了非独特分解的经典理论的基本方面，如Geroldinger和Halter-Koch 2006年专着的主题，以非换向和非取消的环境，以同样的Baeth和Smertnig的工作精神论非换向，但难民载荷的分解理论（Baeth and Smertnig（2015））。然后，我们带来了电力龙眼，应用了第一部分开发的抽象机械，我们对其算法进行了研究。尤其是乘以乘法写的。所有非空的有限子集的setpfin（h）自然地进入了一条多个，我们呼叫电力ofhand是非取消的，除非是微不足道的，通过赋予操作（x，y）？{xy :( x ，y）∈x×y} .Power onoids是伪装，其中一个主要的算术组合对象之一，并且在这里首次从分解理论的角度解决它们。证据导致考虑可以以非平凡的方式分成NNTHAT的有限子集的各种性质，从而产生与添加数字理论的丰富相互作用。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号