dc.contributor.author | Alkan, M. | |
dc.contributor.author | Nicholson, W. K. | |
dc.contributor.author | Ozcan, A. C. | |
dc.date.accessioned | 2019-12-16T09:39:27Z | |
dc.date.available | 2019-12-16T09:39:27Z | |
dc.date.issued | 2011 | |
dc.identifier.issn | 0022-4049 | |
dc.identifier.uri | https://doi.org/10.1016/j.jpaa.2010.11.001 | |
dc.identifier.uri | http://hdl.handle.net/11655/19726 | |
dc.description.abstract | The concept of an enabling ideal is introduced so that an ideal I is strongly lifting if and only if it is lifting and enabling. These ideals are studied and their properties are described. It is shown that a left duo ring is an exchange ring if and only if every ideal is enabling, that Zhou's delta-ideal is always enabling, and that the right singular ideal is enabling if and only if it is contained in the Jacobson radical. The notion of a weakly enabling left ideal is defined, and it is shown that a ring is an exchange ring if and only if every left ideal is weakly enabling. Two related conditions, interesting in themselves, are investigated: the first gives a new characterization of delta-small left ideals, and the second characterizes weakly enabling left ideals. As an application (which motivated the paper), let M be an I-semiregular left module where I is an enabling ideal. It is shown that m is an element of M is I-semiregular if and only if m - q is an element of IM for some regular element q of M and, as a consequence, that if M is countably generated and IM is delta-small in M, then M congruent to circle plus(infinity)(i=1) Rei where e(i)(2) = ei is an element of R for each i. (C) 2010 Elsevier B.V. All rights reserved. | |
dc.language.iso | en | |
dc.publisher | Elsevier Science Bv | |
dc.relation.isversionof | 10.1016/j.jpaa.2010.11.001 | |
dc.rights | info:eu-repo/semantics/openAccess | |
dc.subject | Mathematics | |
dc.title | Strong Lifting Splits | |
dc.type | info:eu-repo/semantics/article | |
dc.type | info:eu-repo/semantics/publishedVersion | |
dc.relation.journal | Journal Of Pure And Applied Algebra | |
dc.contributor.department | Matematik | |
dc.identifier.volume | 215 | |
dc.identifier.issue | 8 | |
dc.identifier.startpage | 1879 | |
dc.identifier.endpage | 1888 | |
dc.description.index | WoS | |
dc.description.index | Scopus | |