Matches in SemOpenAlex for { <https://semopenalex.org/work/W2069725610> ?p ?o ?g. }
Showing items 1 to 48 of
48
with 100 items per page.
- W2069725610 endingPage "85" @default.
- W2069725610 startingPage "73" @default.
- W2069725610 abstract "Let R be a ring with Jacobson radical J. Bass [ 1 ] called R semi-perfect if the factor ring R/J is semi-simple Artinian and every idempotent of R/J can be lifted to an idempotent of R. He showed that R is semi-perfect if and only if every cyclic left R-module has a projective cover and also that this so (if and) only if every finitely generated left R-module has a projective cover. The concept of semi-perfect rings has since then been generalized in two directions: to semi-perfect modules by Mares [3] and to F-semiperfect rings by Oberst and Schneider [6]. A left R-module is called a semi-perfect module if it is projective and every homomorphic image of it has a projective cover. Thus trivially R is a semi-perfect ring if and only if R is semi-perfect as a left R-module, and every finitely generated projective left module over a semi-perfect ring is semi-perfect. The following characterization was obtained: a projective left R-module P is semi-perfect if and only if JP is small in P, the factor module P/JP is completely reducible (=semi-simple), and every direct decomposition of P/JP can be lifted to that of P. On the other hand, a ring R is defined to be F-semi-perfect if the factor ring R/J is a regular ring (in the sence of von Neumann) and every idempotent of R/J can be lifted to an idempotent of R. It was proved that the F-semi-perfectness of R is equivalent to either of the following conditions: (a) every factor module R/Ra has a projective cover for a in R, or (b) every finitely presented left R-module has a projective cover. We attempt in this paper to generalize the concept of F-semi-perfect rings to modules along the line from semi-perfect rings to semi-perfect modules. Namely we call a left R-module P an F-semi-perfect module if B is projective and if, for every endomorphism s of P, the factor module P/Ps" @default.
- W2069725610 created "2016-06-24" @default.
- W2069725610 creator A5056041241 @default.
- W2069725610 date "1991-01-01" @default.
- W2069725610 modified "2023-09-23" @default.
- W2069725610 title "F-semi-perfect modules" @default.
- W2069725610 cites W1970286478 @default.
- W2069725610 cites W1971231024 @default.
- W2069725610 cites W2013620690 @default.
- W2069725610 cites W2023897267 @default.
- W2069725610 cites W2044041144 @default.
- W2069725610 cites W2089627326 @default.
- W2069725610 cites W2148582132 @default.
- W2069725610 cites W3032696613 @default.
- W2069725610 doi "https://doi.org/10.1016/0021-8693(91)90065-g" @default.
- W2069725610 hasPublicationYear "1991" @default.
- W2069725610 type Work @default.
- W2069725610 sameAs 2069725610 @default.
- W2069725610 citedByCount "16" @default.
- W2069725610 countsByYear W20697256102013 @default.
- W2069725610 countsByYear W20697256102016 @default.
- W2069725610 crossrefType "journal-article" @default.
- W2069725610 hasAuthorship W2069725610A5056041241 @default.
- W2069725610 hasConcept C202444582 @default.
- W2069725610 hasConcept C33923547 @default.
- W2069725610 hasConceptScore W2069725610C202444582 @default.
- W2069725610 hasConceptScore W2069725610C33923547 @default.
- W2069725610 hasIssue "1" @default.
- W2069725610 hasLocation W20697256101 @default.
- W2069725610 hasOpenAccess W2069725610 @default.
- W2069725610 hasPrimaryLocation W20697256101 @default.
- W2069725610 hasRelatedWork W1557945163 @default.
- W2069725610 hasRelatedWork W1985218657 @default.
- W2069725610 hasRelatedWork W2023661790 @default.
- W2069725610 hasRelatedWork W2073994398 @default.
- W2069725610 hasRelatedWork W2096753949 @default.
- W2069725610 hasRelatedWork W2742285599 @default.
- W2069725610 hasRelatedWork W2963341196 @default.
- W2069725610 hasRelatedWork W3106133691 @default.
- W2069725610 hasRelatedWork W3124205579 @default.
- W2069725610 hasRelatedWork W4249580765 @default.
- W2069725610 hasVolume "136" @default.
- W2069725610 isParatext "false" @default.
- W2069725610 isRetracted "false" @default.
- W2069725610 magId "2069725610" @default.
- W2069725610 workType "article" @default.