arXiv 1007.02232010-07math.RA

Continuity of homomorphisms on pro-nilpotent algebras

George M. Bergman

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
发表信息：: Illinois J. Math., 55 (2011) 749--770
DOI：: 10.1215/ijm/1369841783

英文摘要：

Let V be a variety of not necessarily associative algebras, and A an inverse limit of nilpotent algebras A_i\in V, such that some finitely generated subalgebra S \subseteq A is dense in A under the inverse limit of the discrete topologies on the A_i. A sufficient condition on V is obtained for all algebra homomorphisms from A to finite-dimensional algebras B to be continuous; in other words, for the kernels of all such homomorphisms to be open ideals. This condition is satisfied, in particular, if V is the variety of associative, Lie, or Jordan algebras. Examples are given showing the need for our hypotheses, and some open questions are noted.

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