Regular sequences in Z2-graded commutative algebra
Regular sequences in Z2-graded commutative algebra
复制标题
Z2 分级交换代数中的正则序列
DOI：
10.1016/0021-8693(89)90153-1
复制
发表时间：
1989
影响因子：
0.9
通讯作者：
T. Schmitt
中科院分区：
文献类型：
--
作者：
T. Schmitt
本文在Z2-分次交换代数（或称“超代数”）的背景下研究了由偶数元和奇数元组成的正则序列。我们将投射空间Pn上的凝聚层P B A与Z2-交换局部环上的每个有限模A相联系，它的支撑包含了A上奇正则序列的所有信息.引入正则局部环的经典概念的Z2-版本，证明了在这类环上，所有极大奇A-正则序列的公共长度与A的极小自由分解中的项的秩的增长有关.我们还调查性质的平坦的局部同态和部分类似的定理Vasconcelos connormalally自由理想。
We investigate regular sequences consisting of even and odd elements in the context of Z 2-graded commutative algebra (or “superalgebra”). We associate to every finite module A over a Z 2-commutative local ring a coherent sheaf P b A on a Projective space P n, and its support contains all information on odd regular sequences on A. We introduce the Z 2-version of the classical notion of regular local rings, and it turns out that over such rings the common length of all maximal odd A-regular sequences is connected with the growth of the ranks of the terms in a minimal free resolution of A. We also investigate properties of flat local homomorphisms and a partial analogue of the theorem of Vasconcelos on conormally free ideals.