Rings whose nonsingular right modules are R-projective
| dc.authorid | alagoz, yusuf/0000-0002-2535-4679 | |
| dc.contributor.author | Alagoz, Yusuf | |
| dc.contributor.author | Benli, Sinem | |
| dc.contributor.author | Buyukasik, Engin | |
| dc.date.accessioned | 2024-12-24T19:30:02Z | |
| dc.date.available | 2024-12-24T19:30:02Z | |
| dc.date.issued | 2021 | |
| dc.department | Siirt Üniversitesi | |
| dc.description.abstract | A right R-module M is called R-projective provided that it is projective relative to the right R-module R-R. This paper deals with the rings whose all nonsingular right modules are R-projective. For a right nonsingular ring R, we prove that R-R is of finite Goldie rank and all nonsingular right R-modules are R-projective if and only if R is right finitely Sigma-CS and fiat right R-modules are R-projective. Then, R-projectivity of the class of nonsingular injective right modules is also considered. Over right nonsingular rings of finite right Goldie rank, it is shown that R-projectivity of nonsingular injective right modules is equivalent to R-projectivity of the injective hull E(R-R). In this case, the injective hull E(R-R) has the decomposition E(R-R) = U-R circle plus V-R, where U is projective and Hom(V, R/I) = 0 for each right ideal I of R. Finally, we focus on the right orthogonal class N-perpendicular to of the class IV of nonsingular right modules. | |
| dc.identifier.doi | 10.14712/1213-7243.2021.036 | |
| dc.identifier.endpage | 407 | |
| dc.identifier.issn | 0010-2628 | |
| dc.identifier.issn | 1213-7243 | |
| dc.identifier.issue | 4 | |
| dc.identifier.scopus | 2-s2.0-85125037468 | |
| dc.identifier.scopusquality | Q4 | |
| dc.identifier.startpage | 393 | |
| dc.identifier.uri | https://doi.org/10.14712/1213-7243.2021.036 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12604/7351 | |
| dc.identifier.volume | 62 | |
| dc.identifier.wos | WOS:000818514600001 | |
| dc.identifier.wosquality | N/A | |
| dc.indekslendigikaynak | Web of Science | |
| dc.indekslendigikaynak | Scopus | |
| dc.language.iso | en | |
| dc.publisher | Charles Univ, Fac Mathematics & Physics | |
| dc.relation.ispartof | Commentationes Mathematicae Universitatis Carolinae | |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.snmz | KA_20241222 | |
| dc.subject | nonsingular module | |
| dc.subject | R-projective module | |
| dc.subject | flat module | |
| dc.subject | perfect ring | |
| dc.title | Rings whose nonsingular right modules are R-projective | |
| dc.type | Article |
