pro-幂零代数上同态的连续性
环与代数
2021-10-15 v3
摘要
设V是一个未必结合的代数簇，A是幂零代数A_i∈V的逆极限，使得某个有限生成的子代数S⊆A在A_i上的离散拓扑的逆极限下在A中稠密。我们得到了V的一个充分条件，使得从A到有限维代数B的所有代数同态都是连续的；换句话说，所有这些同态的核都是开理想。特别地，如果V是结合代数、李代数或若尔当代数的簇，则该条件成立。给出了说明我们的假设必要性的例子，并指出了一些未解决的问题。
引用
@article{arxiv.1007.0223,
title = {Continuity of homomorphisms on pro-nilpotent algebras},
author = {George M. Bergman},
journal= {arXiv preprint arXiv:1007.0223},
year = {2021}
}
备注
Apologies; in submitting version 2, I didn't realize I had to delete version 1; so the result was a mess. Here is the proper revised version. 23 pages, to appear, Ill.J.Math. Main changes in Aug.2010 revision: Re-formatted to fit journal-sized page. New Section 8 added, on question of when subalgebras of finite codimension must be open. Proofs of Lemma 5 and of Lemma 6(iii) shortened