Rings Whose Nonsingular Modules Have Projective Covers
| Autor: | Sh. Asgari, A. Haghany |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Ring (mathematics)
Pure mathematics Property (philosophy) General Mathematics 010102 general mathematics 0102 computer and information sciences 01 natural sciences law.invention Invertible matrix 010201 computation theory & mathematics law Projective cover Von Neumann regular ring Finitely-generated abelian group 0101 mathematics Algebra over a field Projective test Mathematics |
| Zdroj: | Ukrainian Mathematical Journal. 68:1-13 |
| ISSN: | 1573-9376 0041-5995 |
| Popis: | We determine rings R with the property that all (finitely generated) nonsingular right R-modules have projective covers. These are just the rings with t-supplemented (finitely generated) free right modules. Hence, they are called right (finitely) Σ-t-supplemented. It is also shown that a ring R for which every cyclic nonsingular right R-module has a projective cover is exactly a right t-supplemented ring. It is proved that, for a continuous ring R, the property of right Σ- t-supplementedness is equivalent to the semisimplicity of R/Z 2(R R ), while the property of being right finitely Σ- t-supplemented is equivalent to the right self-injectivity of R/Z 2(R R ). Moreover, for a von Neumann regular ring R, the properties of being right Σ- t -supplemented, right finitely Σ- t -supplemented, and right t-supplemented are equivalent to the semisimplicity, right self-injectivity, and right continuity of R, respectively. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|