论文标题
晶格理论特性的替代理想的理想特性
Lattice Theoretic Properties of Aprroximating Ideals
论文作者
论文摘要
事实证明，特殊的预定理想在确切类别$（{\ Mathcal a}; {\ Mathcal e}）$中的有限相交是一个特殊的预定理想。双重的是，特殊的精确理想的有限交集是一种特殊的精确理想。 Happel和Unger的反例表明，关于特殊预先开发子类别的类似陈述在经典近似理论中不存在。如果确切的类别具有确切的副作用，则分别分别为。这些技术产生了bongartz-eklof-trlifaj lemma：如果$ a \ colon a \ to b $是$ {\ mathcal a}中的形态，则是$ {\ mathcal a}，则是理想的$ a^{\ perp} $是特殊的preendeending。这是Eklof-trlifaj引理的理想版本，但证明是基于Bongartz的引理。主要的结果是，由小型理想产生的理想合并对已经完成。
It is proved that a finite intersection of special preenveloping ideals in an exact category $({\mathcal A}; {\mathcal E})$ is a special preenveloping ideal. Dually, a finite intersection of special precovering ideals is a special precovering ideal. A counterexample of Happel and Unger shows that the analogous statement about special preenveloping subcategories does not hold in classical approximation theory. If the exact category has exact coproducts, resp., exact products, these results extend to intersections of infinite families of special peenveloping, resp., special precovering, ideals. These techniques yield the Bongartz-Eklof-Trlifaj Lemma: if $a \colon A \to B$ is a morphism in ${\mathcal A},$ then the ideal $a^{\perp}$ is special preenveloping. This is an ideal version of the Eklof-Trlifaj Lemma, but the proof is based on that of Bongartz' Lemma. The main consequence is that the ideal cotorsion pair generated by a small ideal is complete.
