The Carlitz algebras
- 作者：V.V. Bavula
- 关键词：Context independence ; Weakened WARP ; Top cycle
- 刊名：Journal of Pure and Applied Algebra
- 出版年：2008
- 期刊代码：35_00224049
- 类别：mt
- 出版时间：May 2008
- 卷：212
- 期：5
- 页码：1175-1186
- 文件大小：300 K
摘要
The Carlitz JPD6-1&_mathId=mml1&_user=10&_cdi=5649&_rdoc=17&_acct=C000050221&_version=1&_userid=10&md5=0ce49eb861a52e4616aabe423621e703">
-algebra cct=C000050221&_version=1&_userid=10&md5=e997e699aa7c01f2b50b690a10ffdad7" title="Click to view the MathML source">C=Cν, cct=C000050221&_version=1&_userid=10&md5=cb0c9d80b1c11cc98be8cd665b054359">
, is generated over an algebraically closed field cct=C000050221&_version=1&_userid=10&md5=e407d24ac11ce2b50d63676736168a6e">
(which contains a non-discrete locally compact field of positive characteristic cct=C000050221&_version=1&_userid=10&md5=10cf7477e6dacc645ca4e4ed543b0108" title="Click to view the MathML source">p>0, i.e. cct=C000050221&_version=1&_userid=10&md5=29bc0733ee6f617794c11c6014d06552">
, cct=C000050221&_version=1&_userid=10&md5=ad8fc94fe5d06e85a22b6d4a7a9eb565" title="Click to view the MathML source">q=pν), by the (power of the) Frobenius map cct=C000050221&_version=1&_userid=10&md5=d28eb0ffe603c363e58a460c8d4c2c97" title="Click to view the MathML source">X=Xν:f
fq, and by the Carlitz derivative cct=C000050221&_version=1&_userid=10&md5=d7247c5ad3db200776bcce0924773a1b" title="Click to view the MathML source">Y=Yν. It is proved that the Krull and global dimensions of cct=C000050221&_version=1&_userid=10&md5=5956f411a2b188cf3ef1d3746690ed50" title="Click to view the MathML source">C are 2, classifications of simple cct=C000050221&_version=1&_userid=10&md5=00f189f25dd1bae5300dc7bee0ff8906" title="Click to view the MathML source">C-modules and ideals are given, there are only countably many ideals, they commute cct=C000050221&_version=1&_userid=10&md5=459ef6d7a120745c183c2814de32911e" title="Click to view the MathML source">(IJ=JI), and each ideal is a unique product of maximal ones. It is a remarkable fact that any simple cct=C000050221&_version=1&_userid=10&md5=997416b22980c6ba63566da8441b1aa6" title="Click to view the MathML source">C-module is a sum of eigenspaces of the element cct=C000050221&_version=1&_userid=10&md5=d65929d671c66c55ea1ab9ccaa523be2" title="Click to view the MathML source">YX (the set of eigenvalues for cct=C000050221&_version=1&_userid=10&md5=f75962e26d0b270181701cddf689a4de" title="Click to view the MathML source">YX is given explicitly for each simple cct=C000050221&_version=1&_userid=10&md5=cb5607e37a9c697d5afa8ac4b0fd1b36" title="Click to view the MathML source">C-module). This fact is crucial in finding the group cct=C000050221&_version=1&_userid=10&md5=345f10b3752e7042415c108ff17c0b50">
of cct=C000050221&_version=1&_userid=10&md5=47f0d47e88c07dc8f93e605dcb5583c7">
-algebra automorphisms of cct=C000050221&_version=1&_userid=10&md5=cc31b9d236da3927fb8614b67297554e" title="Click to view the MathML source">C and in proving that any two distinct Carlitz rings are not isomorphic (cct=C000050221&_version=1&_userid=10&md5=755e7506f0cf10335a6a77c260562d12" title="Click to view the MathML source">Cν
Cμ if cct=C000050221&_version=1&_userid=10&md5=02eda5c0b4ae8f0513a453e60d24dabc" title="Click to view the MathML source">ν≠μ). The centre of cct=C000050221&_version=1&_userid=10&md5=85e48a12374c09933d4bea6b633f24e7" title="Click to view the MathML source">C is found explicitly, it is a UFD that contains countably many elements.
fq, and by the Carlitz derivative cct=C000050221&_version=1&_userid=10&md5=d7247c5ad3db200776bcce0924773a1b" title="Click to view the MathML source">Y=Yν. It is proved that the Krull and global dimensions of cct=C000050221&_version=1&_userid=10&md5=5956f411a2b188cf3ef1d3746690ed50" title="Click to view the MathML source">C are 2, classifications of simple cct=C000050221&_version=1&_userid=10&md5=00f189f25dd1bae5300dc7bee0ff8906" title="Click to view the MathML source">C-modules and ideals are given, there are only countably many ideals, they commute cct=C000050221&_version=1&_userid=10&md5=459ef6d7a120745c183c2814de32911e" title="Click to view the MathML source">(IJ=JI), and each ideal is a unique product of maximal ones. It is a remarkable fact that any simple cct=C000050221&_version=1&_userid=10&md5=997416b22980c6ba63566da8441b1aa6" title="Click to view the MathML source">C-module is a sum of eigenspaces of the element cct=C000050221&_version=1&_userid=10&md5=d65929d671c66c55ea1ab9ccaa523be2" title="Click to view the MathML source">YX (the set of eigenvalues for cct=C000050221&_version=1&_userid=10&md5=f75962e26d0b270181701cddf689a4de" title="Click to view the MathML source">YX is given explicitly for each simple cct=C000050221&_version=1&_userid=10&md5=cb5607e37a9c697d5afa8ac4b0fd1b36" title="Click to view the MathML source">C-module). This fact is crucial in finding the group cct=C000050221&_version=1&_userid=10&md5=345f10b3752e7042415c108ff17c0b50">Cμ if cct=C000050221&_version=1&_userid=10&md5=02eda5c0b4ae8f0513a453e60d24dabc" title="Click to view the MathML source">ν≠μ). The centre of cct=C000050221&_version=1&_userid=10&md5=85e48a12374c09933d4bea6b633f24e7" title="Click to view the MathML source">C is found explicitly, it is a UFD that contains countably many elements.