当前位置:
X-MOL 学术
›
Czechoslov. Math. J.
›
论文详情
Our official English website, www.x-mol.net, welcomes your
feedback! (Note: you will need to create a separate account there.)
A Class of Multiplicative Lattices
Czechoslovak Mathematical Journal ( IF 0.4 ) Pub Date : 2021-03-15 , DOI: 10.21136/cmj.2021.0034-20 Tiberiu Dumitrescu , Mihai Epure
中文翻译:
一类乘法格
更新日期:2021-04-11
Czechoslovak Mathematical Journal ( IF 0.4 ) Pub Date : 2021-03-15 , DOI: 10.21136/cmj.2021.0034-20 Tiberiu Dumitrescu , Mihai Epure
We study the multiplicative lattices L which satisfy the condition a = (a: (a: b))(a: b) for all a, b ∈ L. Call them sharp lattices. We prove that every totally ordered sharp lattice is isomorphic to the ideal lattice of a valuation domain with value group ℤ or ℝ. A sharp lattice L localized at its maximal elements are totally ordered sharp lattices. The converse is true if L has finite character.
中文翻译:
一类乘法格
我们研究的乘法格子大号满足条件一个=(一个:(一:b())一:b为全部)的a,b ∈大号。称他们为锋利的格子。我们证明,每个完全有序的尖晶格都与值域为ℤ或group的估值域的理想晶格同构。定位在其最大元素处的尖晶格L是完全有序的尖晶格。如果L具有有限字符,则相反。