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Division closed ℓ-rings and power positive L∗-rings
Quaestiones Mathematicae ( IF 0.6 ) Pub Date : 2020-06-02 , DOI: 10.2989/16073606.2020.1766595 Jingjing Ma 1 , Brandi Rygaard 2
中文翻译:
除法闭ℓ-环和幂正L∗-环
更新日期:2020-06-02
Quaestiones Mathematicae ( IF 0.6 ) Pub Date : 2020-06-02 , DOI: 10.2989/16073606.2020.1766595 Jingjing Ma 1 , Brandi Rygaard 2
Affiliation
Abstract
A commutative non-associative division closed lattice-ordered ring with identity that is not an f -ring is presented. More conditions are provided to ensure that an associative division closed lattice-ordered ring is an f -ring. In particular, for a division closed lattice-ordered ring with identity, if it is Σ-clean or Σ-semiclean, then it is an f -ring. Finally it is shown that a ring with identity in which each partial order can be extended to a lattice order satisfying (x2n)− = 0 for some integer n ≥ 1 must be an O*-ring.
中文翻译:
除法闭ℓ-环和幂正L∗-环
摘要
提出了一个身份不是f环的可交换非结合除法闭合格序环。提供了更多条件以确保关联划分闭晶格有序环是f环。特别是,对于具有恒等式的除法闭晶格有序环,如果它是 Σ-clean 或 Σ-semiclean,那么它就是一个f环。最后表明,对于某个整数n ≥ 1 ,其中每个偏序都可以扩展到满足 ( x 2 n ) − = 0的格序的具有身份的环必须是O * 环。