论文标题
$ \ mathfrak {m} $ - baer和$ \ mathfrak {M} $ - Rickart Lattices
$\mathfrak{m}$-Baer and $\mathfrak{m}$-Rickart lattices
论文作者
论文摘要
在本文中，我们介绍了Rickart和Baer Lattices及其双重的概念。我们表明，只需使用晶格理论中的技术就可以理解里卡特和贝尔模块理论的一部分。对于，我们使用T. Albu和M. Iosif引入的线性形态。我们专注于一个零$ \ mathfrak {m} $的subonoid，这是晶格$ \ mathcal {l} $的所有线性内态性的单体，以提供更通用的方法并将我们的结果应用于模块理论。我们还表明，$ \ mathfrak {m} $ - rickart和$ \ mathfrak {m} $ - baer lattices可以由$ \ mathfrak {m} $ baer lattices来表征由$ \ mathfrak {m} $产生的，就像模块一样。
In this paper we introduce the notions of Rickart and Baer lattices and their duals. We show that part of the theory of Rickart and Baer modules can be understood just using techniques from the theory of lattices. For, we use linear morphisms introduced by T. Albu and M. Iosif. We focus on a submonoid with zero $\mathfrak{m}$ of the monoid of all linear endomorphism of a lattice $\mathcal{L}$ in order to give a more general approach and apply our results in the theory of modules. We also show that $\mathfrak{m}$-Rickart and $\mathfrak{m}$-Baer lattices can be characterized by the annihilators in $\mathfrak{m}$ generated by idempotents as in the case of modules.
