From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1412 Path: news.gmane.org!not-for-mail From: Jiri Rosicky Newsgroups: gmane.science.mathematics.categories Subject: flat covers Date: Wed, 9 Feb 2000 14:08:06 +0100 (CET) Message-ID: <200002091308.OAA24141@bart.math.muni.cz> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241017814 31143 80.91.229.2 (29 Apr 2009 15:10:14 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:10:14 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed Feb 9 20:16:32 2000 -0400 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id TAA09750 for categories-list; Wed, 9 Feb 2000 19:21:13 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Mailer: ELM [version 2.4ME+ PL69 (25)] Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 12 Xref: news.gmane.org gmane.science.mathematics.categories:1412 Archived-At: The flat cover conjecture was formulated by E. Enochs in 1981 and asks whether every module has a flat cover. In his paper, he also showed that it is equivalent to weak coreflectivity of flat modules in modules. In 1995, J. Xu has proved that it is true over commutative noetherian rings of finite Krull dimension. The flat cover conjecture has been recently proved (over an arbitrary ring) by L. Bican, R. El Bashir and E. Enochs. In a paper "Flat covers and factorizations", I am giving a purely categorical proof based on the theorem of J. Smith about weak factorization systems. Jiri Rosicky