论文标题
$ \ mathbb {z}/m \ mathbb {z} $中的dempotents的算术
Arithmetic of idempotents in $\mathbb{Z}/m \mathbb{Z}$
论文作者
论文摘要
依恋元素是戒指理论的一个充分研究的部分，在$ \ mathbb {z}/m \ mathbb {z} $中具有几种diadempotents的身份。尽管在添加的情况下，依恋素材并未关闭，但仍然有一些有趣的添加剂身份可以得出和使用。在本文中，我们在$ \ mathbb {z}/ m \ mathbb {z} $中提供了几个新的身份。我们将所有整数$ k $的有限sublatices与$ \ mathbb {z}/ k \ mathbb {z} $与无限晶格相关联，该晶格嵌入了$ \ mathbb {n} $上的划分晶格中，并彼此相同，并以此无限lattice lattite lattite lattite lattite lattite lattite lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice lattice。使用此关系，我们将$ \ Mathbb {Z}/M \ Mathbb {Z} $中的几个身份推广到与这些有限sublattices相关的iDempotents的人。最后，作为上述基本身份的应用，我们得出了一种用于计算$ \ mathbb {z}/ m \ mathbb {z} $的算法。
Idempotent elements are a well-studied part of ring theory, with several identities of the idempotents in $\mathbb{Z}/m\mathbb{Z}$ already known. Although the idempotents are not closed under addition, there are still interesting additive identities that can be derived and used. In this paper, we give several new identities on idempotents in $\mathbb{Z}/ m\mathbb{Z}$. We relate finite sublattices over $\mathbb{Z}/ k\mathbb{Z}$ for all integers $k$ to an infinite lattice that is embedded in the divisibility lattice on $\mathbb{N}$ and to each other as sublattices of this infinite lattice. Using this relation, we generalize several identities on idempotents in $\mathbb{Z}/m\mathbb{Z}$ to those involving idempotents related to these finite sublattices. Finally, as an application of the above idempotent identities, we derive an algorithm for calculating modular exponentiation over $\mathbb{Z}/ m\mathbb{Z}$.
