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The lattice R-tors for perfect rings.
Rincón-Mejía, H. A.

Data: 1989
Resum: We define ̃F in R-tors by r ̃F σ iff the class of r-codivisible modules coincides with the class of σ -codivisible modules. We prove that if R is left perfect ring (resp. semiperfect ring) then every [r] f Є R-tors/ ̃F (resp. [X]F and [ε]F) is a complete sublattice of R-tors We describe the largest element in [r] as X(Rad R/t,(Rad R)) and the least element of [r] as ε (t r(RadR)) Using these results we give a necessary and sufficient condition for the central splitting of Goldman torsion theory when R is semiperfect. We prove that for a QF ring R the least element of [X] ̃F is the Goldie torsion theory. This can be used to prove that for a QF ring ̃F and ̃T are equal, where r ̃T o iff the class of r-injective modules coincides with the class of σ-injective modules .
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: article ; recerca ; publishedVersion
Publicat a: Publicacions Matemàtiques, V. 33 n. 1 (1989) p. 17-35, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_33189_02

19 p, 471.2 KB

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