论文标题
使用交换环的一些BL-Elgebras的例子
Some examples of BL-algebras using commutative rings
论文作者
论文摘要
本文的目的是使用交换环对BL-Elgebras的结构进行分析。从计算考虑因素来看，我们对有限情况非常感兴趣。我们提出了使用交换戒指生成有限的BL-Elgebras的新方法，并总结了统计数据。 此外，我们研究了BL环，即，理想的晶格可以配备BL-Elgebra的结构。这些戒指的新特征及其与其他类别的戒指的连接得以建立。另外，我们举例说明了有限的bl环的示例，其理想的晶格不是MV-Elgebra，并且使用这些环，我们用$ 2^{r}+1 $元素构造了Bl-Elgebras，$ r \ geq 2，$ r \ geq 2，$ and $ a $ k $ elements，$ k $ 4. $ 4 $ $ 4. $ 4. $4。
The aim of this paper is to analize the structure of BL-algebras using commutative rings. From computational considerations, we are very interested in the finite case. We present new ways to generate finite BL-algebras using commutative rings and we give summarizing statistics. Furthermore, we investigated BL-rings, i.e., commutative rings whose the lattice of ideals can be equiped with a structure of BL-algebra. A new characterization for these rings and their connections to other classes of rings are established. Also, we give examples of finite BL-rings for which their lattice of ideals is not an MV-algebra and using these rings we construct BL-algebras with $2^{r}+1$ elements, $r\geq 2,$ and \ all BL-chains with $k$ elements, $k\geq 4.$
