Finite matrix topologies

[摘要] A filter F of positive-primitive formulae may be used to give a right R-module M-R the structure M-F of a topological abelian group. The topology is called a finite matrix topology if every finite matrix subgroup Of M-R is closed in M-F. It is shown that the pure-injective envelope is functorial on the subcategory of modules for which M-F is dense in its pure-injective envelope. We call a right R-module almost pure-injective if there is a filter F with respect to which the topological abelian group M-F is dense in its pure-injective envelope [PE(M)](F). In that case, every R-endomorphism of PE(M-R) is determined by its restriction to M-R. When M = R-R, this gives the pure-injective envelope PE(R-R) a ring structure extending that of R, and the proof of this result suggests that this ring is the pure variation of the ring of quotients of a nonsingular ring. (C) 2004 Published by Elsevier Inc.

[发布日期] 2004-12-01

[关键词] finite matrix subgroup;positive-primitive formula;topological abelian group;pure-injective envelope