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- Title
Rings Whose Nonsingular Modules Have Projective Covers.
- Authors
Asgari, Sh.; Haghany, A.
- Abstract
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 ( R ) , while the property of being right finitely Σ- t-supplemented is equivalent to the right self-injectivity of R/Z ( 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.
- Subjects
RING theory; MATHEMATICAL singularities; MODULES (Algebra); VON Neumann regular rings; PATHS &; cycles in graph theory
- Publication
Ukrainian Mathematical Journal, 2016, Vol 68, Issue 1, p1
- ISSN
0041-5995
- Publication type
Article
- DOI
10.1007/s11253-016-1204-7