论文标题
Nakayama代数的有限维度
The finitistic dimension of a Nakayama algebra
论文作者
论文摘要
如果A是Artin代数，则Gélinas为A的有限尺寸引入了一个有趣的上限，即Delooping Level del A.我们断言，对于任何Nakayama代数，其有限尺寸等于Del A.这也等于A。这也会产生一个新的证据，即在Al Gergebra的相反范围内，如果Sem均与SEN相等，那么SEN。在S及其注入式信封的投影维度（其中一个必须是有限的）； E*（s）S及其投影覆盖物的注入尺寸的最小值。那么A的有限维度是数字E（S）的最大值以及数字E^*（S）的最大值。 使用合适的syzygy模块，我们构造了简单模块的置换h，使得e*（h（s））= e（s）。特别是，这显示了任何自然数z，具有e（s）= z的简单模块的数量等于with e（s'）= z的简单模块s'的数量。
If A is an artin algebra, Gélinas has introduced an interesting upper bound for the finitistic dimension of A, namely the delooping level del A. We assert that for any Nakayama algebra, its finitistic dimension is equal to del A. This yields also a new proof that the finitistic dimension of A and of its opposite algebra are equal, as shown recently by Sen. If S is a simple module, let e(S) be the minimum of the projective dimension of S and of its injective envelope (one of these numbers has to be finite); and e*(S) the minimum of the injective dimension of S and of its projective cover. Then the finitistic dimension of A is the maximum of the numbers e(S) as well as the maximum of the numbers e^*(S). Using suitable syzygy modules, we construct a permutation h of the simple modules S such that e*(h(S)) = e(S). In particular, this shows for any natural number z, that the number of simple modules S with e(S) = z is equal to the number of simple modules S' with e(S') = z.
