Unique factorization monoids and domains
Unique factorization monoids and domains
复制标题
独特的因式分解幺半群和域
DOI：
10.1090/s0002-9939-1971-0277453-7
复制
发表时间：
1971
影响因子：
0.6
通讯作者：
R. E. Johnson
中科院分区：
文献类型：
--
作者：
R. E. Johnson
本文的目的是构造唯一的因子分解么半群和整环。主要结果是：(1)良序么半群的自由积是UF-么半群当且仅当该集合中的每个么半群都是UF-么半群。(2)如果M是有序么半群，F是域，则具有良序支撑的所有形式幂级数的环F[AI]是UF-整环当且仅当M是自然序的(即，每当b1}。有序么半群M称为自然序的当且仅当aMnbM$0和b<；a，然后是aMCbM。本文的目的是给出构造Uf么半群和UF-整环的方法。两个主要结果如下。定理1.良序么半群的自由积是UF-么半群，如果集合中的每个么半群都是UF-么半群。定理2.设M是有序么半群，F是域。如果M是自然序的，则所有有良序支集的形式幂级数的环F[[M]]都是ufdomain。由编辑于1970年4月27日收到。AMS 1970学科分类。小学16A02，20M25；中学06A50。
It is the purpose of this paper to construct unique factorization (uf) monoids and domains. The principal results are: (1) The free product of a well-ordered set of monoids is a uf-monoid iff every monoid in the set is a uf-monoid. (2) If M is an ordered monoid and F is a field, the ring F [AI] ] of all formal power series with well-ordered support is a uf-domain iff M is naturally ordered (i.e., whenever b 1 }. An ordered monoid M is said to be naturally ordered (see [4, p. 154]) iff whenever aMnbM$0 and b<a, then aMCbM. It is the purpose of this paper to show ways of constructing ufmonoids and uf-domains. The two principal results are as follows. THEOREM 1. The free product of a well-ordered set of monoids is a uf-monoid if every monoid in the set is a uf-monoid. THEOREM 2. Let M be an ordered monoid and F be a field. The ring F[[M]] of all formal power series with well-ordered support is a ufdomain if M is naturally ordered. Received by the editors April 27, 1970. AMS 1970 subject classifications. Primary 16A02, 20M25; Secondary 06A50.