Open AccessA NOTE ON FLAT MODULES OVER $f$-ALGEBRAS
Author(s) -
Boris Lavrič
Publication year - 1991
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.22.1991.4625
Subject(s) - mathematics , unital , ideal (ethics) , ring (chemistry) , pure mathematics , maximal ideal , type (biology) , algebra over a field , discrete mathematics , combinatorics , ecology , philosophy , chemistry , organic chemistry , epistemology , biology
Let $A$ be an Archimedean uniformly complete unital $f$-algebra.It is proved that the following conditions are equivalent: (1) $A$ is a Bezout ring; (2) $A$ is a PF-ring; (3) Every ideal of $A$ is flat; (4) Every submodule of a free $A$-module is flat. This extends a result by C. Neville on algebras of type $C(X)$.