Subalgebras that are cyclic as submodules |
| |
Authors: | Helmut Röhrl Manfred Bernd Wischnewsky |
| |
Affiliation: | (1) Department of Mathematics, University of California, 92093 La Jolla, California, USA;(2) Fachsektion Mathematik, Universität Achterstr., D-28 Bermen 33, Germany |
| |
Abstract: | Let R be an associative, commutative, unital ring. By a R-algebra we mean a unital R-module A together with a R-module homomorphism : RnAA (n2). We raise the question whether such an algebra possesses either an idempotent or a nilpotent element. In section 1 an affirmative answer is obtained in case R=k is an algebraically closed field and dimkA<, as well as in case R=, dimS<, and n0(2). Section 2 deals with the case of reduced rings R and R-algebras which are finitely generated and projective as R-modules. In section 3 we show that the generic algebra over an integral domain D fails to have nilpotent elements in any integral domain extending its base ring Dn,m, and thus acquires an idempotent element in some integral domain extending Dn,m.Partially supported by National Science Foundation Grant GP-38229. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|