Extending Ring Derivations to Right and Symmetric Rings and Modules of Quotients
نویسندگان
چکیده
منابع مشابه
Extending Ring Derivations to Right and Symmetric Rings and Modules of Quotients
We define and study the symmetric version of differential torsion theories. We prove that the symmetric versions of some of the existing results on derivations on right modules of quotients hold for derivations on symmetric modules of quotients. In particular, we prove that the symmetric Lambek, Goldie and perfect torsion theories are differential. We also study conditions under which a derivat...
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A torsion theory is called differential (higher differential) if a derivation (higher derivation) can be extended from any module to the module of quotients corresponding to the torsion theory. We study conditions equivalent to higher differentiability of a torsion theory. It is known that the Lambek, Goldie and any perfect torsion theories are differential. We show that these classes of torsio...
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15 صفحه اولHigher derivations on rings and modules
Let τ be a hereditary torsion theory on ModR and suppose that Qτ : ModR → ModR is the localization functor. It is shown that for all R-modules M, every higher derivation defined on M can be extended uniquely to a higher derivation defined on Qτ(M) if and only if τ is a higher differential torsion theory. It is also shown that if τ is a TTF theory and Cτ : M →M is the colocalization functor, the...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2009
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927870802271664